# Who's up to the challenge? 7

Algebra Level 4

You're given that $$\frac { 1 }{ n } +\frac { 1 }{ k } =1$$ 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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