Excel in math, science, and engineering

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Given that \(x\) and \(y\) are positive real such that \(x+y=1\), find the value of \(k\) such that the maximum value of \({ x }^{ 4 }y+x{ y }^{ 4 }\) is \(\dfrac { 1 }{ k }\).This is not a original problem

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