# Who's up to the challenge? 7

Algebra Level 4

You're given that $$\dfrac 1n +\dfrac 1k =1$$ and that $$n=4$$. If the sum $$\displaystyle\sum _{ i=1 }^{ m }{ { x }_{ i }^{ n } } =1296$$ and the sum $$\displaystyle\sum _{ i=1 }^{ m }{ { y }_{ i }^{ k } } =16$$ then find the maximum value of $$\displaystyle \sum _{ i=1 }^{ m }{ { x }_{ i }{ y }_{ i } }$$.

Note: All $${x}_{i}$$ and $${y}_{i}$$ are non-negative real numbers.

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