Inequality is back

Let $x_1,x_2,x_3,x_4 \in \mathbb{R^{+}}$ such that $x_1x_2x_3x_4=1$.

Prove that :

$\large{\displaystyle \sum_{i=1}^{4} x_i^{3} \geq \text{max.}\left(\displaystyle \sum_{i=1}^4 x_i , \displaystyle \sum_{i=1}^4 \dfrac1{x_i}\right)}$

Easy Math Editor

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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}`	$\boxed{123}$

Comments

@Rahil Sehgal Here is another one..

Ankit Kumar Jain - 4 years, 1 month ago

Please post your solutions everyone...

Ankit Kumar Jain - 4 years, 1 month 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}`	$\boxed{123}$