Proof Contest Day 6

Due to some problem yesterday, day 6 question is now on.

Suppose $x,y,z,w$ are positive reals such that

$\large{\begin{cases} { x }^{ 2 }+{ y }^{ 2 }-\frac { xy }{ 2 } ={ w }^{ 2 }+{ z }^{ 2 }+\frac { wz }{ 2 } =36 \\ xz+yw=30 \end{cases}}$

Prove that

$\large{ (xy+wz)^{2} \le 960 }$

#Algebra

Easy Math Editor

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Comments

Since Nobody posted the solution here is the proof.

Department 8 - 5 years, 5 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}`	$\boxed{123}$