# Who's up to the challenge? 9

Algebra Level 4

Given that $$\displaystyle\sum _{ n=1 }^{ k }{ { x }_{ n }^{ 2 } } =9$$ and that $$\displaystyle\sum _{ n=1 }^{ k }{ { y }_{ n }^{ 2 } } =5329$$

Find the maximum value of $$\displaystyle\sum _{ n=1 }^{ k }{ { ({ x }_{ n }+{ y }_{ n }) }^{ 2 } }$$.

Note: $${x}_{n},{y}_{n}\ge0$$.

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