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# 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

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

Note by Lakshya Sinha
2 years ago

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Since Nobody posted the solution here is the proof.

- 2 years ago