Prove that abcd>=3

nice

Advertisements

stand of Shur’s inequality

nice number

A generalization of Nesbitt’s Inequality

last two digit

very nice problem by van khea

old inequality

ineq problem

2013

បីរបៀបសំរាប់ស្រាយបញ្ចាក់វិសមភាព

ineq_0001ineq_0002

វិសមភាពសំរាប់សិស្សពូកែ

(vankhea) គេអោយបីចំនួនពិតវិជ្ជមាន a, b, c ផ្ទៀងផ្ទាត់ a+b+c=3. បង្ហាញថាៈ
\displaystyle \frac{a^k}{\sqrt{pb+qc}}+\frac{b^k}{\sqrt{pc+qa}}+\frac{c^k}{\sqrt{pa+qb}}\geq \frac{3}{\sqrt{p+q}}
\displaystyle \forall{p, q>0} and \displaystyle \forall{k\geq \frac{3}{2}-\frac{ln2}{2(ln3-ln2)}}