Maximum Holds When \(a=b=c=d\), Right?

Algebra Level 3

Let \(a,b,c\) and \(d\) be real numbers satisfying \[a^4+b^4+c^4+d^4=16\; . \] Find the maximum value of \[a^5+b^5+c^5+d^5 \; . \]

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