Really, is very large!!!

Here comes the problem,

Let $a,b,c$ be real non-negative numbers, prove that:

$a+b+c\le \frac { { a }^{ 2 }+{ b }^{ 2 } }{ 2c } +\frac { { b }^{ 2 }+{ c }^{ 2 } }{ 2a } +\frac { { c }^{ 2 }+{ a }^{ 2 } }{ 2b } \le \frac { { a }^{ 3 } }{ bc } +\frac { { b }^{ 3 } }{ ca } +\frac { { c }^{ 3 } }{ ab }$

#Algebra #Inequalities #Muirhead

Easy Math Editor

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Whenever u see cyclic homogeneous inequality. Think of EMV theorem. It helps to prove this ineq in 3lines....

Dinesh Chavan - 6 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$