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	<title>ចំណេះដឹងនិងចំណេះធ្វើ !!!</title>
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		<title>ចំណេះដឹងនិងចំណេះធ្វើ !!!</title>
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		<title>សំរាយបញ្ជាក់វិសមភាព AM-GM ងាយៗ</title>
		<link>http://kheavan.wordpress.com/2012/01/10/%e1%9e%9f%e1%9f%86%e1%9e%9a%e1%9e%b6%e1%9e%99%e1%9e%94%e1%9e%89%e1%9f%92%e1%9e%87%e1%9e%b6%e1%9e%80%e1%9f%8b%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96-am-gm-%e1%9e%84%e1%9e%b6/</link>
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		<pubDate>Tue, 10 Jan 2012 19:29:07 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាជុំវិញពិភពលោក]]></category>

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			<content:encoded><![CDATA[<p><a href="http://kheavan.wordpress.com/2012/01/10/%e1%9e%9f%e1%9f%86%e1%9e%9a%e1%9e%b6%e1%9e%99%e1%9e%94%e1%9e%89%e1%9f%92%e1%9e%87%e1%9e%b6%e1%9e%80%e1%9f%8b%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96-am-gm-%e1%9e%84%e1%9e%b6/vankhea2012_0001/" rel="attachment wp-att-6377"><img class="aligncenter size-large wp-image-6377" title="vankhea201" src="http://kheavan.files.wordpress.com/2012/01/vankhea2012_0001.jpg?w=791&#038;h=1024" alt="" width="791" height="1024" /></a></p>
<br />Filed under: <a href='http://kheavan.wordpress.com/category/%e1%9e%82%e1%9e%8e%e1%9e%b7%e1%9e%8f%e1%9e%9c%e1%9e%b7%e1%9e%91%e1%9f%92%e1%9e%99%e1%9e%b6%e1%9e%87%e1%9e%bb%e1%9f%86%e1%9e%9c%e1%9e%b7%e1%9e%89%e1%9e%96%e1%9e%b7%e1%9e%97%e1%9e%96%e1%9e%9b%e1%9f%84/'>គណិតវិទ្យាជុំវិញពិភពលោក</a>  <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gocomments/kheavan.wordpress.com/6376/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/comments/kheavan.wordpress.com/6376/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godelicious/kheavan.wordpress.com/6376/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/delicious/kheavan.wordpress.com/6376/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gofacebook/kheavan.wordpress.com/6376/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/facebook/kheavan.wordpress.com/6376/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gotwitter/kheavan.wordpress.com/6376/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/twitter/kheavan.wordpress.com/6376/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gostumble/kheavan.wordpress.com/6376/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/stumble/kheavan.wordpress.com/6376/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godigg/kheavan.wordpress.com/6376/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/digg/kheavan.wordpress.com/6376/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/goreddit/kheavan.wordpress.com/6376/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/reddit/kheavan.wordpress.com/6376/" /></a> <img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6376&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></content:encoded>
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		<slash:comments>1</slash:comments>
	
		<media:content url="http://1.gravatar.com/avatar/14a2f834f8be0c9465bb020abab89396?s=96&#38;d=http%3A%2F%2F1.gravatar.com%2Favatar%2Fad516503a11cd5ca435acc9bb6523536%3Fs%3D96&#38;r=G" medium="image">
			<media:title type="html">kheavan</media:title>
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			<media:title type="html">vankhea201</media:title>
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	</item>
		<item>
		<title>Problem 315 vankhea</title>
		<link>http://kheavan.wordpress.com/2011/12/18/problem-315-vankhea/</link>
		<comments>http://kheavan.wordpress.com/2011/12/18/problem-315-vankhea/#comments</comments>
		<pubDate>Sun, 18 Dec 2011 22:09:55 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាផ្នែកវិសមភាព]]></category>

		<guid isPermaLink="false">http://kheavan.wordpress.com/?p=6367</guid>
		<description><![CDATA[គេអោយបីចំនួនពិតវិជ្ជមាន ផ្ទៀងផ្ទាត់ ។ ស្រាយបញ្ជាក់ថាៈ Filed under: គណិតវិទ្យាផ្នែកវិសមភាព<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6367&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>គេអោយបីចំនួនពិតវិជ្ជមាន <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> ផ្ទៀងផ្ទាត់ <img src='http://s0.wp.com/latex.php?latex=a%5E2%2Bb%5E2%2Bc%5E2%3D1&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a^2+b^2+c^2=1' title='a^2+b^2+c^2=1' class='latex' /> ។ ស្រាយបញ្ជាក់ថាៈ<br />
<img src='http://s0.wp.com/latex.php?latex=7%28a%5E3%2Bb%5E3%2Bc%5E3%29%2B33abc%5Cleq+6%28a%2Bb%2Bc%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='7(a^3+b^3+c^3)+33abc&#92;leq 6(a+b+c)' title='7(a^3+b^3+c^3)+33abc&#92;leq 6(a+b+c)' class='latex' /></p>
<br />Filed under: <a href='http://kheavan.wordpress.com/category/%e1%9e%82%e1%9e%8e%e1%9e%b7%e1%9e%8f%e1%9e%9c%e1%9e%b7%e1%9e%91%e1%9f%92%e1%9e%99%e1%9e%b6%e1%9e%95%e1%9f%92%e1%9e%93%e1%9f%82%e1%9e%80%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96/'>គណិតវិទ្យាផ្នែកវិសមភាព</a>  <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gocomments/kheavan.wordpress.com/6367/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/comments/kheavan.wordpress.com/6367/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godelicious/kheavan.wordpress.com/6367/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/delicious/kheavan.wordpress.com/6367/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gofacebook/kheavan.wordpress.com/6367/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/facebook/kheavan.wordpress.com/6367/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gotwitter/kheavan.wordpress.com/6367/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/twitter/kheavan.wordpress.com/6367/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gostumble/kheavan.wordpress.com/6367/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/stumble/kheavan.wordpress.com/6367/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godigg/kheavan.wordpress.com/6367/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/digg/kheavan.wordpress.com/6367/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/goreddit/kheavan.wordpress.com/6367/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/reddit/kheavan.wordpress.com/6367/" /></a> <img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6367&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></content:encoded>
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		<slash:comments>0</slash:comments>
	
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			<media:title type="html">kheavan</media:title>
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		<item>
		<title>Problem 314 vankhea</title>
		<link>http://kheavan.wordpress.com/2011/12/18/problem-314-vankhea-2/</link>
		<comments>http://kheavan.wordpress.com/2011/12/18/problem-314-vankhea-2/#comments</comments>
		<pubDate>Sun, 18 Dec 2011 22:06:57 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាផ្នែកវិសមភាព]]></category>

		<guid isPermaLink="false">http://kheavan.wordpress.com/?p=6364</guid>
		<description><![CDATA[គេអោយបីចំនួនពិតវិជ្ជមាន ផ្ទៀងផ្ទាត់ ។ ស្រាយបញ្ជាក់ថាៈ Filed under: គណិតវិទ្យាផ្នែកវិសមភាព<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6364&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>គេអោយបីចំនួនពិតវិជ្ជមាន <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> ផ្ទៀងផ្ទាត់ <img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+abc%3D%5Cfrac%7B7%7D%7B141%7D&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle abc=&#92;frac{7}{141}' title='&#92;displaystyle abc=&#92;frac{7}{141}' class='latex' /> ។ ស្រាយបញ្ជាក់ថាៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%28a%2Bb%2Bc%29%5E3%5Cgeq+%5Cfrac%7B7%7D%7B6%7D%28a%5E3%2Bb%5E3%2Bc%5E3%2B1%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle (a+b+c)^3&#92;geq &#92;frac{7}{6}(a^3+b^3+c^3+1)' title='&#92;displaystyle (a+b+c)^3&#92;geq &#92;frac{7}{6}(a^3+b^3+c^3+1)' class='latex' /></p>
<br />Filed under: <a href='http://kheavan.wordpress.com/category/%e1%9e%82%e1%9e%8e%e1%9e%b7%e1%9e%8f%e1%9e%9c%e1%9e%b7%e1%9e%91%e1%9f%92%e1%9e%99%e1%9e%b6%e1%9e%95%e1%9f%92%e1%9e%93%e1%9f%82%e1%9e%80%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96/'>គណិតវិទ្យាផ្នែកវិសមភាព</a>  <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gocomments/kheavan.wordpress.com/6364/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/comments/kheavan.wordpress.com/6364/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godelicious/kheavan.wordpress.com/6364/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/delicious/kheavan.wordpress.com/6364/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gofacebook/kheavan.wordpress.com/6364/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/facebook/kheavan.wordpress.com/6364/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gotwitter/kheavan.wordpress.com/6364/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/twitter/kheavan.wordpress.com/6364/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gostumble/kheavan.wordpress.com/6364/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/stumble/kheavan.wordpress.com/6364/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godigg/kheavan.wordpress.com/6364/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/digg/kheavan.wordpress.com/6364/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/goreddit/kheavan.wordpress.com/6364/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/reddit/kheavan.wordpress.com/6364/" /></a> <img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6364&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></content:encoded>
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		<slash:comments>0</slash:comments>
	
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			<media:title type="html">kheavan</media:title>
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	</item>
		<item>
		<title>Problem 313 van khea</title>
		<link>http://kheavan.wordpress.com/2011/12/10/problem-313-van-khea/</link>
		<comments>http://kheavan.wordpress.com/2011/12/10/problem-313-van-khea/#comments</comments>
		<pubDate>Sat, 10 Dec 2011 15:41:28 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាផ្នែកវិសមភាព]]></category>

		<guid isPermaLink="false">http://kheavan.wordpress.com/?p=6340</guid>
		<description><![CDATA[គេអោយ ជាបីចំនួនពិតវិជ្ជមានផ្ទៀងផ្ទាត់ ។ ស្រាយបញ្ជាក់ថាៈ Filed under: គណិតវិទ្យាផ្នែកវិសមភាព<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6340&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>គេអោយ <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> ជាបីចំនួនពិតវិជ្ជមានផ្ទៀងផ្ទាត់ <img src='http://s0.wp.com/latex.php?latex=a%2Bb%2Bc%3D3&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a+b+c=3' title='a+b+c=3' class='latex' /> ។ ស្រាយបញ្ជាក់ថាៈ<br />
<img src='http://s0.wp.com/latex.php?latex=a%5E4%2Bb%5E4%2Bc%5E4%2B18%5Cgeq+2%28a%5E3%2Bb%5E3%2Bc%5E3%29%2B15abc&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a^4+b^4+c^4+18&#92;geq 2(a^3+b^3+c^3)+15abc' title='a^4+b^4+c^4+18&#92;geq 2(a^3+b^3+c^3)+15abc' class='latex' /></p>
<br />Filed under: <a href='http://kheavan.wordpress.com/category/%e1%9e%82%e1%9e%8e%e1%9e%b7%e1%9e%8f%e1%9e%9c%e1%9e%b7%e1%9e%91%e1%9f%92%e1%9e%99%e1%9e%b6%e1%9e%95%e1%9f%92%e1%9e%93%e1%9f%82%e1%9e%80%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96/'>គណិតវិទ្យាផ្នែកវិសមភាព</a>  <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gocomments/kheavan.wordpress.com/6340/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/comments/kheavan.wordpress.com/6340/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godelicious/kheavan.wordpress.com/6340/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/delicious/kheavan.wordpress.com/6340/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gofacebook/kheavan.wordpress.com/6340/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/facebook/kheavan.wordpress.com/6340/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gotwitter/kheavan.wordpress.com/6340/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/twitter/kheavan.wordpress.com/6340/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gostumble/kheavan.wordpress.com/6340/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/stumble/kheavan.wordpress.com/6340/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godigg/kheavan.wordpress.com/6340/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/digg/kheavan.wordpress.com/6340/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/goreddit/kheavan.wordpress.com/6340/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/reddit/kheavan.wordpress.com/6340/" /></a> <img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6340&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></content:encoded>
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			<media:title type="html">kheavan</media:title>
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		<title>Problem 312 Crux</title>
		<link>http://kheavan.wordpress.com/2011/12/10/problem-312-crux/</link>
		<comments>http://kheavan.wordpress.com/2011/12/10/problem-312-crux/#comments</comments>
		<pubDate>Sat, 10 Dec 2011 11:22:23 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាផ្នែកវិសមភាព]]></category>

		<guid isPermaLink="false">http://kheavan.wordpress.com/?p=6338</guid>
		<description><![CDATA[គេអោយបីចំនួនពិតវិជ្ជមាន មានផលបូលស្មើនឹង 3 ។ ស្រាយបញ្ជាក់ថាៈ Filed under: គណិតវិទ្យាផ្នែកវិសមភាព<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6338&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>គេអោយបីចំនួនពិតវិជ្ជមាន <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> មានផលបូលស្មើនឹង 3 ។ ស្រាយបញ្ជាក់ថាៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B1%7D%7B9-ab%7D%2B%5Cfrac%7B1%7D%7B9-bc%7D%2B%5Cfrac%7B1%7D%7B9-ca%7D%5Cleq+%5Cfrac%7B3%7D%7B8%7D&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;frac{1}{9-ab}+&#92;frac{1}{9-bc}+&#92;frac{1}{9-ca}&#92;leq &#92;frac{3}{8}' title='&#92;displaystyle &#92;frac{1}{9-ab}+&#92;frac{1}{9-bc}+&#92;frac{1}{9-ca}&#92;leq &#92;frac{3}{8}' class='latex' /></p>
<br />Filed under: <a href='http://kheavan.wordpress.com/category/%e1%9e%82%e1%9e%8e%e1%9e%b7%e1%9e%8f%e1%9e%9c%e1%9e%b7%e1%9e%91%e1%9f%92%e1%9e%99%e1%9e%b6%e1%9e%95%e1%9f%92%e1%9e%93%e1%9f%82%e1%9e%80%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96/'>គណិតវិទ្យាផ្នែកវិសមភាព</a>  <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gocomments/kheavan.wordpress.com/6338/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/comments/kheavan.wordpress.com/6338/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godelicious/kheavan.wordpress.com/6338/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/delicious/kheavan.wordpress.com/6338/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gofacebook/kheavan.wordpress.com/6338/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/facebook/kheavan.wordpress.com/6338/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gotwitter/kheavan.wordpress.com/6338/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/twitter/kheavan.wordpress.com/6338/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gostumble/kheavan.wordpress.com/6338/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/stumble/kheavan.wordpress.com/6338/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godigg/kheavan.wordpress.com/6338/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/digg/kheavan.wordpress.com/6338/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/goreddit/kheavan.wordpress.com/6338/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/reddit/kheavan.wordpress.com/6338/" /></a> <img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6338&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></content:encoded>
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			<media:title type="html">kheavan</media:title>
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		<title>Problem 311 Moldova TST 2005</title>
		<link>http://kheavan.wordpress.com/2011/12/10/problem-311-moldova-tst-2005/</link>
		<comments>http://kheavan.wordpress.com/2011/12/10/problem-311-moldova-tst-2005/#comments</comments>
		<pubDate>Sat, 10 Dec 2011 11:16:28 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាផ្នែកវិសមភាព]]></category>

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		<description><![CDATA[ស្រាយបញ្ជាក់ថាបើ ជាបីចំនួនពិតវិជ្ជមានហើយ នោះគេបានៈ Filed under: គណិតវិទ្យាផ្នែកវិសមភាព<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6336&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>ស្រាយបញ្ជាក់ថាបើ <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> ជាបីចំនួនពិតវិជ្ជមានហើយ <img src='http://s0.wp.com/latex.php?latex=a%5E4%2Bb%5E4%2Bc%5E4%3D3&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a^4+b^4+c^4=3' title='a^4+b^4+c^4=3' class='latex' /> នោះគេបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B1%7D%7B4-ab%7D%2B%5Cfrac%7B1%7D%7B4-bc%7D%2B%5Cfrac%7B1%7D%7B4-ca%7D%5Cleq+1&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;frac{1}{4-ab}+&#92;frac{1}{4-bc}+&#92;frac{1}{4-ca}&#92;leq 1' title='&#92;displaystyle &#92;frac{1}{4-ab}+&#92;frac{1}{4-bc}+&#92;frac{1}{4-ca}&#92;leq 1' class='latex' /></p>
<br />Filed under: <a href='http://kheavan.wordpress.com/category/%e1%9e%82%e1%9e%8e%e1%9e%b7%e1%9e%8f%e1%9e%9c%e1%9e%b7%e1%9e%91%e1%9f%92%e1%9e%99%e1%9e%b6%e1%9e%95%e1%9f%92%e1%9e%93%e1%9f%82%e1%9e%80%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96/'>គណិតវិទ្យាផ្នែកវិសមភាព</a>  <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gocomments/kheavan.wordpress.com/6336/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/comments/kheavan.wordpress.com/6336/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godelicious/kheavan.wordpress.com/6336/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/delicious/kheavan.wordpress.com/6336/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gofacebook/kheavan.wordpress.com/6336/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/facebook/kheavan.wordpress.com/6336/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gotwitter/kheavan.wordpress.com/6336/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/twitter/kheavan.wordpress.com/6336/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gostumble/kheavan.wordpress.com/6336/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/stumble/kheavan.wordpress.com/6336/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godigg/kheavan.wordpress.com/6336/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/digg/kheavan.wordpress.com/6336/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/goreddit/kheavan.wordpress.com/6336/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/reddit/kheavan.wordpress.com/6336/" /></a> <img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6336&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></content:encoded>
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			<media:title type="html">kheavan</media:title>
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		<title>Problem 310 vankhea</title>
		<link>http://kheavan.wordpress.com/2011/12/09/problem-310-vankhea/</link>
		<comments>http://kheavan.wordpress.com/2011/12/09/problem-310-vankhea/#comments</comments>
		<pubDate>Fri, 09 Dec 2011 23:45:13 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាផ្នែកវិសមភាព]]></category>

		<guid isPermaLink="false">http://kheavan.wordpress.com/?p=6330</guid>
		<description><![CDATA[គេអោយ ជាបីចំនួនពិតវិជ្ជមាន។ ស្រាយថាៈ សំរាយបញ្ជាក់ៈ យើងមានៈ គុណអង្គទាំងពីរនឹង នោះយើងបានៈ ដូចគ្នាដែរយើងបានៈ បូកអង្គនឹងអង្គនៃវិសមភាពខាងលើយើងបានៈ Filed under: គណិតវិទ្យាផ្នែកវិសមភាព<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6330&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>គេអោយ <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> ជាបីចំនួនពិតវិជ្ជមាន។ ស្រាយថាៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%28a%5E2%2Bb%5E2%29%5E2%2B%28b%5E2%2Bc%5E2%29%5E2%2B%28c%5E2%2Ba%5E2%29%5E2%5Cgeq+4%28a%5E3b%2Bb%5E3c%2Bc%5E3a%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='(a^2+b^2)^2+(b^2+c^2)^2+(c^2+a^2)^2&#92;geq 4(a^3b+b^3c+c^3a)' title='(a^2+b^2)^2+(b^2+c^2)^2+(c^2+a^2)^2&#92;geq 4(a^3b+b^3c+c^3a)' class='latex' /><br />
សំរាយបញ្ជាក់ៈ<br />
យើងមានៈ <img src='http://s0.wp.com/latex.php?latex=%28a-b%29%5E2%5Cgeq+0%5CRightarrow+a%5E2%2Bb%5E2%5Cgeq+2ab&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='(a-b)^2&#92;geq 0&#92;Rightarrow a^2+b^2&#92;geq 2ab' title='(a-b)^2&#92;geq 0&#92;Rightarrow a^2+b^2&#92;geq 2ab' class='latex' /><br />
គុណអង្គទាំងពីរនឹង <img src='http://s0.wp.com/latex.php?latex=2a%5E2&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='2a^2' title='2a^2' class='latex' /> នោះយើងបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=2a%5E4%2B2a%5E2b%5E2%5Cgeq+4a%5E3b&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='2a^4+2a^2b^2&#92;geq 4a^3b' title='2a^4+2a^2b^2&#92;geq 4a^3b' class='latex' /><br />
ដូចគ្នាដែរយើងបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=2b%5E4%2B2b%5E2c%5E2%5Cgeq+4b%5E3c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='2b^4+2b^2c^2&#92;geq 4b^3c' title='2b^4+2b^2c^2&#92;geq 4b^3c' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=2c%5E4%2B2c%5E2a%5E2%5Cgeq+4c%5E3a&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='2c^4+2c^2a^2&#92;geq 4c^3a' title='2c^4+2c^2a^2&#92;geq 4c^3a' class='latex' /><br />
បូកអង្គនឹងអង្គនៃវិសមភាពខាងលើយើងបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=2%28a%5E4%2Bb%5E4%2Bc%5E4%29%2B2%28a%5E2b%5E2%2Bb%5E2c%5E2%2Bc%5E2a%5E2%29%5Cgeq+4%28a%5E3b%2Bb%5E3c%2Bc%5E3a%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='2(a^4+b^4+c^4)+2(a^2b^2+b^2c^2+c^2a^2)&#92;geq 4(a^3b+b^3c+c^3a)' title='2(a^4+b^4+c^4)+2(a^2b^2+b^2c^2+c^2a^2)&#92;geq 4(a^3b+b^3c+c^3a)' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=%5CLeftrightarrow+%28a%5E2%2Bb%5E2%29%5E2%2B%28b%5E2%2Bc%5E2%29%5E2%2B%28c%5E2%2Ba%5E2%29%5E2%5Cgeq+4%28a%5E3b%2Bb%5E3c%2Bc%5E3a%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;Leftrightarrow (a^2+b^2)^2+(b^2+c^2)^2+(c^2+a^2)^2&#92;geq 4(a^3b+b^3c+c^3a)' title='&#92;Leftrightarrow (a^2+b^2)^2+(b^2+c^2)^2+(c^2+a^2)^2&#92;geq 4(a^3b+b^3c+c^3a)' class='latex' /></p>
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		<title>Problem 309 van khea</title>
		<link>http://kheavan.wordpress.com/2011/12/07/problem-309-van-khea/</link>
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		<pubDate>Wed, 07 Dec 2011 17:05:39 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាផ្នែកវិសមភាព]]></category>

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		<description><![CDATA[គេអោយបីចំនួនពិតវិជ្ជមាន ផ្ទៀងផ្ទាត់ៈ ។ ស្រាយបញ្ជាក់ថាៈ សំរាយបញ្ជាក់ ជាដំបូងយើងត្រូវស្រាយថា គុណអង្គទាំងពីរនឹង នោះយើងបានៈ ចែកអង្គទាំងពីរនឹង នោះយើងបានៈ តាង នោះវិសមភាពខាងលើសមមូលនឹងៈ ដោយ ដូចនេះយើងបានៈ ពិតជានិច្ច។ ដូចគ្នាដែរយើងបាន និង បូកអង្គនិងអង្គនៃវិសមភាពខាងលើយើងបានៈ ដូចនេះយើងបាន ពិតជានិច្ច។ ដូចនេះវិសមភាពត្រូវបានស្រាយបញ្ជាក់។ សមភាពកើតមានពេល Filed under: គណិតវិទ្យាផ្នែកវិសមភាព<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6314&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>គេអោយបីចំនួនពិតវិជ្ជមាន <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> ផ្ទៀងផ្ទាត់ៈ <img src='http://s0.wp.com/latex.php?latex=a%2Bb%2Bc%3D3&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a+b+c=3' title='a+b+c=3' class='latex' /> ។ ស្រាយបញ្ជាក់ថាៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%5Csqrt%7B1%2Ba%5E4%7D%2B%5Csqrt%7B1%2Bb%5E4%7D%2B%5Csqrt%7B1%2Bc%5E4%7D%5Cleq+%5Csqrt%7B2%7D%28a%5E2%2Bb%5E2%2Bc%5E2%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;sqrt{1+a^4}+&#92;sqrt{1+b^4}+&#92;sqrt{1+c^4}&#92;leq &#92;sqrt{2}(a^2+b^2+c^2)' title='&#92;sqrt{1+a^4}+&#92;sqrt{1+b^4}+&#92;sqrt{1+c^4}&#92;leq &#92;sqrt{2}(a^2+b^2+c^2)' class='latex' /><br />
សំរាយបញ្ជាក់<br />
ជាដំបូងយើងត្រូវស្រាយថា <img src='http://s0.wp.com/latex.php?latex=%5Csqrt%7B1%2Ba%5E4%7D%5Cleq+%5Csqrt%7B2%7D%28a%5E2-a%2B1%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;sqrt{1+a^4}&#92;leq &#92;sqrt{2}(a^2-a+1)' title='&#92;sqrt{1+a^4}&#92;leq &#92;sqrt{2}(a^2-a+1)' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5CLeftrightarrow+%28a%5E2-a%2B1%29%5E2%5Cgeq+%5Cfrac%7B1%7D%7B2%7D%281%2Ba%5E4%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;Leftrightarrow (a^2-a+1)^2&#92;geq &#92;frac{1}{2}(1+a^4)' title='&#92;displaystyle &#92;Leftrightarrow (a^2-a+1)^2&#92;geq &#92;frac{1}{2}(1+a^4)' class='latex' /><br />
គុណអង្គទាំងពីរនឹង <img src='http://s0.wp.com/latex.php?latex=%281%2Ba%29%5E2&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='(1+a)^2' title='(1+a)^2' class='latex' /> នោះយើងបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%28a%5E2-a%2B1%29%5E2%281%2Ba%29%5E2%5Cgeq+%5Cfrac%7B1%7D%7B2%7D%281%2Ba%5E4%29%281%2Ba%29%5E2&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle (a^2-a+1)^2(1+a)^2&#92;geq &#92;frac{1}{2}(1+a^4)(1+a)^2' title='&#92;displaystyle (a^2-a+1)^2(1+a)^2&#92;geq &#92;frac{1}{2}(1+a^4)(1+a)^2' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5CLeftrightarrow+%281%2Ba%5E3%29%5E2+%5Cgeq+%5Cfrac%7B1%7D%7B2%7D%281%2Ba%5E4%29%281%2Ba%29%5E2&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;Leftrightarrow (1+a^3)^2 &#92;geq &#92;frac{1}{2}(1+a^4)(1+a)^2' title='&#92;displaystyle &#92;Leftrightarrow (1+a^3)^2 &#92;geq &#92;frac{1}{2}(1+a^4)(1+a)^2' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5CLeftrightarrow+a%5E6%2B1%2B2a%5E3%5Cgeq+%5Cfrac%7B1%7D%7B2%7D%281%2Ba%5E4%29%281%2Ba%29%5E2&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;Leftrightarrow a^6+1+2a^3&#92;geq &#92;frac{1}{2}(1+a^4)(1+a)^2' title='&#92;displaystyle &#92;Leftrightarrow a^6+1+2a^3&#92;geq &#92;frac{1}{2}(1+a^4)(1+a)^2' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5CRightarrow+a%5E6%2B1%2Ba%5E2%281%2Ba%29%5E2%5Cgeq+a%5E2%281%2Ba%5E2%29%2B%5Cfrac%7B1%7D%7B2%7D%281%2Ba%5E4%29%281%2Ba%29%5E2&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;Rightarrow a^6+1+a^2(1+a)^2&#92;geq a^2(1+a^2)+&#92;frac{1}{2}(1+a^4)(1+a)^2' title='&#92;displaystyle &#92;Rightarrow a^6+1+a^2(1+a)^2&#92;geq a^2(1+a^2)+&#92;frac{1}{2}(1+a^4)(1+a)^2' class='latex' /><br />
ចែកអង្គទាំងពីរនឹង <img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B%281%2Ba%29%5E6%7D%7B8%7D&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;frac{(1+a)^6}{8}' title='&#92;displaystyle &#92;frac{(1+a)^6}{8}' class='latex' /> នោះយើងបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B8a%5E6%7D%7B%281%2Ba%29%5E6%7D%2B%5Cfrac%7B8%7D%7B%281%2Ba%29%5E6%7D%2B%5Cfrac%7B8a%5E2%7D%7B%281%2Ba%29%5E4%7D%5Cgeq+%5Cfrac%7B8a%5E2%281%2Ba%5E2%29%7D%7B%281%2Ba%29%5E6%7D%2B%5Cfrac%7B4%281%2Ba%5E4%29%7D%7B%281%2Ba%29%5E4%7D&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;frac{8a^6}{(1+a)^6}+&#92;frac{8}{(1+a)^6}+&#92;frac{8a^2}{(1+a)^4}&#92;geq &#92;frac{8a^2(1+a^2)}{(1+a)^6}+&#92;frac{4(1+a^4)}{(1+a)^4}' title='&#92;displaystyle &#92;frac{8a^6}{(1+a)^6}+&#92;frac{8}{(1+a)^6}+&#92;frac{8a^2}{(1+a)^4}&#92;geq &#92;frac{8a^2(1+a^2)}{(1+a)^6}+&#92;frac{4(1+a^4)}{(1+a)^4}' class='latex' /><br />
តាង <img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+x%3D%5Cfrac%7B2a%5E2%7D%7B%281%2Ba%29%5E2%7D%3B+y%3D%5Cfrac%7B2%7D%7B%281%2Ba%29%5E2%7D&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle x=&#92;frac{2a^2}{(1+a)^2}; y=&#92;frac{2}{(1+a)^2}' title='&#92;displaystyle x=&#92;frac{2a^2}{(1+a)^2}; y=&#92;frac{2}{(1+a)^2}' class='latex' /> នោះវិសមភាពខាងលើសមមូលនឹងៈ<br />
<img src='http://s0.wp.com/latex.php?latex=x%5E3%2By%5E3%2B2xy%5Cgeq+xy%28x%2By%29%2Bx%5E2%2By%5E2&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='x^3+y^3+2xy&#92;geq xy(x+y)+x^2+y^2' title='x^3+y^3+2xy&#92;geq xy(x+y)+x^2+y^2' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=x%5E3-x%5E2%2By%5E3-y%5E3%2B2xy-xy%28x%2By%29%5Cgeq+0&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='x^3-x^2+y^3-y^3+2xy-xy(x+y)&#92;geq 0' title='x^3-x^2+y^3-y^3+2xy-xy(x+y)&#92;geq 0' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=x%5E2%28x-1%29%2By%5E2%28y-1%29-xy%28x-1%29-xy%28y-1%29%5Cgeq+0&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='x^2(x-1)+y^2(y-1)-xy(x-1)-xy(y-1)&#92;geq 0' title='x^2(x-1)+y^2(y-1)-xy(x-1)-xy(y-1)&#92;geq 0' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=x%28x-1%29%28x-y%29%2By%28y-1%29%28y-x%29%5Cgeq+0&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='x(x-1)(x-y)+y(y-1)(y-x)&#92;geq 0' title='x(x-1)(x-y)+y(y-1)(y-x)&#92;geq 0' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=%28x-1%29%5E2%28x%2By-1%29%5Cgeq+0&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='(x-1)^2(x+y-1)&#92;geq 0' title='(x-1)^2(x+y-1)&#92;geq 0' class='latex' /><br />
ដោយ <img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B1%2Ba%5E2%7D%7B2%7D%5Cgeq+%28%5Cfrac%7B1%2Ba%7D%7B2%7D%29%5E2%5CLeftrightarrow+%5Cfrac%7B2a%5E2%7D%7B%281%2Ba%29%5E2%7D%2B%5Cfrac%7B2%7D%7B%281%2Ba%29%5E2%7D%5Cgeq+1&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle &#92;frac{1+a^2}{2}&#92;geq (&#92;frac{1+a}{2})^2&#92;Leftrightarrow &#92;frac{2a^2}{(1+a)^2}+&#92;frac{2}{(1+a)^2}&#92;geq 1' title='&#92;displaystyle &#92;frac{1+a^2}{2}&#92;geq (&#92;frac{1+a}{2})^2&#92;Leftrightarrow &#92;frac{2a^2}{(1+a)^2}+&#92;frac{2}{(1+a)^2}&#92;geq 1' class='latex' /><img src='http://s0.wp.com/latex.php?latex=%5CRightarrow+x%2By%5Cgeq+1&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;Rightarrow x+y&#92;geq 1' title='&#92;Rightarrow x+y&#92;geq 1' class='latex' /><br />
ដូចនេះយើងបានៈ <img src='http://s0.wp.com/latex.php?latex=%28x-1%29%5E2%28x%2By-1%29%5Cgeq+0&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='(x-1)^2(x+y-1)&#92;geq 0' title='(x-1)^2(x+y-1)&#92;geq 0' class='latex' /> ពិតជានិច្ច។<br />
ដូចគ្នាដែរយើងបាន <img src='http://s0.wp.com/latex.php?latex=%5Csqrt%7B1%2Bb%5E4%7D%5Cleq+%5Csqrt%7B2%7D%28b%5E2-b%2B1%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;sqrt{1+b^4}&#92;leq &#92;sqrt{2}(b^2-b+1)' title='&#92;sqrt{1+b^4}&#92;leq &#92;sqrt{2}(b^2-b+1)' class='latex' /> និង <img src='http://s0.wp.com/latex.php?latex=%5Csqrt%7B1%2Bc%5E4%7D%5Cleq+%5Csqrt%7B2%7D%28c%5E2-c%2B1%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;sqrt{1+c^4}&#92;leq &#92;sqrt{2}(c^2-c+1)' title='&#92;sqrt{1+c^4}&#92;leq &#92;sqrt{2}(c^2-c+1)' class='latex' /><br />
បូកអង្គនិងអង្គនៃវិសមភាពខាងលើយើងបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%5Csqrt%7B1%2Ba%5E4%7D%2B%5Csqrt%7B1%2Bb%5E4%7D%2B%5Csqrt%7B1%2Bc%5E4%7D%5Cleq+%5Csqrt%7B2%7D%28a%5E2%2Bb%5E2%2Bc%5E2%2B3-a-b-c%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;sqrt{1+a^4}+&#92;sqrt{1+b^4}+&#92;sqrt{1+c^4}&#92;leq &#92;sqrt{2}(a^2+b^2+c^2+3-a-b-c)' title='&#92;sqrt{1+a^4}+&#92;sqrt{1+b^4}+&#92;sqrt{1+c^4}&#92;leq &#92;sqrt{2}(a^2+b^2+c^2+3-a-b-c)' class='latex' /><br />
ដូចនេះយើងបាន <img src='http://s0.wp.com/latex.php?latex=%5Csqrt%7B1%2Ba%5E4%7D%2B%5Csqrt%7B1%2Bb%5E4%7D%2B%5Csqrt%7B1%2Bc%5E4%7D%5Cleq+%5Csqrt%7B2%7D%28a%5E2%2Bb%5E2%2Bc%5E2%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;sqrt{1+a^4}+&#92;sqrt{1+b^4}+&#92;sqrt{1+c^4}&#92;leq &#92;sqrt{2}(a^2+b^2+c^2)' title='&#92;sqrt{1+a^4}+&#92;sqrt{1+b^4}+&#92;sqrt{1+c^4}&#92;leq &#92;sqrt{2}(a^2+b^2+c^2)' class='latex' /> ពិតជានិច្ច។<br />
ដូចនេះវិសមភាពត្រូវបានស្រាយបញ្ជាក់។ សមភាពកើតមានពេល <img src='http://s0.wp.com/latex.php?latex=a%3Db%3Dc%3D1&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a=b=c=1' title='a=b=c=1' class='latex' /></p>
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		<title>វិសមភាព 2011.8 vankhea និងអនុត្តន៍</title>
		<link>http://kheavan.wordpress.com/2011/12/04/%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96-2011-8-vankhea-%e1%9e%93%e1%9e%b7%e1%9e%84%e1%9e%a2%e1%9e%93%e1%9e%bb%e1%9e%8f%e1%9f%92%e1%9e%8f%e1%9e%93%e1%9f%8d/</link>
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		<pubDate>Sun, 04 Dec 2011 03:48:40 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
				<category><![CDATA[គណិតវិទ្យាផ្នែកវិសមភាព]]></category>
		<category><![CDATA[សៀវភៅ]]></category>

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		<description><![CDATA[នៅក្នុងគណិតវិទ្យា វិសមភាពជាផ្នែកមួយដែលសំបូរទៅដោយលំហាត់ប្លែកៗរាប់មិនអស់ ហើយទ្រឹស្ដីបទក៏ច្រើនមិនអាចកត់សំគាល់បាន។ ហើយនៅថ្ងៃនេះខ្ញុំនឹងលើកយកវិសមភាពមួយបែបដែលវាមានប្រយោជន៍នៅក្នុងគណិតវិទ្យាដែរ ដែលខ្ញុំដាក់ឈ្មោះអោយវិសមភាពនោះថា វិសមភាព 2011.8 vankhea ដែលមានអត្ថន័យថាៈ វិសមភាពត្រូវបានបង្កើតឡើងនៅឆ្នាំ 2011 ខែ 8 ដោយ vankhea ។ វិសមភាព 2011.8 vankhea ចែងដូចខាងក្រោមៈ ចំពោះបណ្ដាចំនួនពិតវិជ្ជមាន គេបានៈ វិសមភាពខាងលើវាមានទំរង់ស្រដៀងគ្នាទៅនឹងវិសមភាព Schur ដែលវិសមភាព Schur បានចែងថាៈ ចំពោះបណ្ដាចំនួនពិតវិជ្ជមាន គេបានៈ វិសមភាពទាំងពីរខាងលើគឺសំរាប់អនុវត្តន៍ក្នុងការដោះស្រាយលំហាត់នៃចំនួនពិតវិជ្ចមាន។ ការអនុវត្តន៍របស់វាគឺទាមទារអោយយើងបំលែងរាល់អថេរនីមួយនៃវិសមភាពអោយចូលក្នុងទ្រឹស្ដីបទខាងលើ។ ដើម្បីអោយកាន់តែច្បាស់ពីការអនុត្តន៍មិត្តអ្នកអានអាចទាញយកឯកសារខាងក្រោមៈ free download 2011.8 vankhea Filed under: គណិតវិទ្យាផ្នែកវិសមភាព, សៀវភៅ<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6297&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>នៅក្នុងគណិតវិទ្យា វិសមភាពជាផ្នែកមួយដែលសំបូរទៅដោយលំហាត់ប្លែកៗរាប់មិនអស់ ហើយទ្រឹស្ដីបទក៏ច្រើនមិនអាចកត់សំគាល់បាន។ ហើយនៅថ្ងៃនេះខ្ញុំនឹងលើកយកវិសមភាពមួយបែបដែលវាមានប្រយោជន៍នៅក្នុងគណិតវិទ្យាដែរ ដែលខ្ញុំដាក់ឈ្មោះអោយវិសមភាពនោះថា វិសមភាព 2011.8 vankhea ដែលមានអត្ថន័យថាៈ វិសមភាពត្រូវបានបង្កើតឡើងនៅឆ្នាំ 2011 ខែ 8 ដោយ vankhea ។<br />
វិសមភាព 2011.8 vankhea ចែងដូចខាងក្រោមៈ<br />
ចំពោះបណ្ដាចំនួនពិតវិជ្ជមាន <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> គេបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%28a%5E2%2Bb%5E2%2Bc%5E2%29%5E2%2B3abc%28a%2Bb%2Bc%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='(a^2+b^2+c^2)^2+3abc(a+b+c)' title='(a^2+b^2+c^2)^2+3abc(a+b+c)' class='latex' /><img src='http://s0.wp.com/latex.php?latex=%5Cleq+3ab%28a%5E2%2Bb%5E2%29%2B3bc%28b%5E2%2Bc%5E2%29%2B3ca%28c%5E2%2Ba%5E2%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;leq 3ab(a^2+b^2)+3bc(b^2+c^2)+3ca(c^2+a^2)' title='&#92;leq 3ab(a^2+b^2)+3bc(b^2+c^2)+3ca(c^2+a^2)' class='latex' /><br />
វិសមភាពខាងលើវាមានទំរង់ស្រដៀងគ្នាទៅនឹងវិសមភាព Schur ដែលវិសមភាព Schur បានចែងថាៈ<br />
ចំពោះបណ្ដាចំនួនពិតវិជ្ជមាន <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> គេបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=a%5E4%2Bb%5E4%2Bc%5E4%2Babc%28a%2Bb%2Bc%29%5Cgeq+ab%28a%5E2%2Bb%5E2%29%2Bbc%28b%5E2%2Bc%5E2%29%2Bca%28c%5E2%2Ba%5E2%29&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a^4+b^4+c^4+abc(a+b+c)&#92;geq ab(a^2+b^2)+bc(b^2+c^2)+ca(c^2+a^2)' title='a^4+b^4+c^4+abc(a+b+c)&#92;geq ab(a^2+b^2)+bc(b^2+c^2)+ca(c^2+a^2)' class='latex' /><br />
វិសមភាពទាំងពីរខាងលើគឺសំរាប់អនុវត្តន៍ក្នុងការដោះស្រាយលំហាត់នៃចំនួនពិតវិជ្ចមាន។ ការអនុវត្តន៍របស់វាគឺទាមទារអោយយើងបំលែងរាល់អថេរនីមួយនៃវិសមភាពអោយចូលក្នុងទ្រឹស្ដីបទខាងលើ។<br />
ដើម្បីអោយកាន់តែច្បាស់ពីការអនុត្តន៍មិត្តអ្នកអានអាចទាញយកឯកសារខាងក្រោមៈ</p>
<h2 style="text-align:center;">
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<br />Filed under: <a href='http://kheavan.wordpress.com/category/%e1%9e%82%e1%9e%8e%e1%9e%b7%e1%9e%8f%e1%9e%9c%e1%9e%b7%e1%9e%91%e1%9f%92%e1%9e%99%e1%9e%b6%e1%9e%95%e1%9f%92%e1%9e%93%e1%9f%82%e1%9e%80%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96/'>គណិតវិទ្យាផ្នែកវិសមភាព</a>, <a href='http://kheavan.wordpress.com/category/%e1%9e%9f%e1%9f%80%e1%9e%9c%e1%9e%97%e1%9f%85/'>សៀវភៅ</a>  <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gocomments/kheavan.wordpress.com/6297/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/comments/kheavan.wordpress.com/6297/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godelicious/kheavan.wordpress.com/6297/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/delicious/kheavan.wordpress.com/6297/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gofacebook/kheavan.wordpress.com/6297/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/facebook/kheavan.wordpress.com/6297/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gotwitter/kheavan.wordpress.com/6297/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/twitter/kheavan.wordpress.com/6297/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/gostumble/kheavan.wordpress.com/6297/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/stumble/kheavan.wordpress.com/6297/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/godigg/kheavan.wordpress.com/6297/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/digg/kheavan.wordpress.com/6297/" /></a> <a rel="nofollow" href="http://feeds.wordpress.com/1.0/goreddit/kheavan.wordpress.com/6297/"><img alt="" border="0" src="http://feeds.wordpress.com/1.0/reddit/kheavan.wordpress.com/6297/" /></a> <img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6297&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></content:encoded>
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		<title>Problem 308 van khea</title>
		<link>http://kheavan.wordpress.com/2011/12/04/problem-308-van-khea/</link>
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		<pubDate>Sun, 04 Dec 2011 01:09:28 +0000</pubDate>
		<dc:creator>van khea</dc:creator>
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		<description><![CDATA[ស្រាយបញ្ជាក់ថាចំពោះបណ្ដាចំនួនពិតវិជ្ជមាន គេបានៈ download answer Filed under: គណិតវិទ្យាផ្នែកវិសមភាព<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=kheavan.wordpress.com&amp;blog=10932190&amp;post=6293&amp;subd=kheavan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>ស្រាយបញ្ជាក់ថាចំពោះបណ្ដាចំនួនពិតវិជ្ជមាន <img src='http://s0.wp.com/latex.php?latex=a%2C+b%2C+c&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='a, b, c' title='a, b, c' class='latex' /> គេបានៈ<br />
<img src='http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+a%5E3%2Bb%5E3%2Bc%5E3%2B15abc%5Cleq+%5Cfrac%7B2%7D%7B3%7D%28a%2Bb%2Bc%29%5E3&amp;bg=fafcff&amp;fg=2a2a2a&amp;s=1' alt='&#92;displaystyle a^3+b^3+c^3+15abc&#92;leq &#92;frac{2}{3}(a+b+c)^3' title='&#92;displaystyle a^3+b^3+c^3+15abc&#92;leq &#92;frac{2}{3}(a+b+c)^3' class='latex' /></p>
<h2 style="text-align:left;"><a href="http://kheavan.wordpress.com/2011/12/04/%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96-2011-8-vankhea-%e1%9e%93%e1%9e%b7%e1%9e%84%e1%9e%a2%e1%9e%93%e1%9e%bb%e1%9e%8f%e1%9f%92%e1%9e%8f%e1%9e%93%e1%9f%8d/2011-8-van-khea/" rel="attachment wp-att-6298">download answer</a></h2>
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