# Differentiation or inequality?

Algebra Level 5

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 $$\dfrac { 1 }{ k }$$.

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