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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