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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
8 months, 2 weeks ago

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Since Nobody posted the solution here is the proof.

Lakshya Sinha · 8 months, 2 weeks ago

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