Finding Both Minimum And Maximum

Algebra Level 5

{x+y+z=4x2+y2+z2=6\large\begin{cases} x+y+z=4\\ x^2+y^2+z^2=6\end{cases}

If x,yx,y and zz are reals numbers that satisfy the system of equations above, find the sum of the maximum and the minimum value of A=x6+y6+z6A= x^6+y^6+z^6.

Round your answer to the nearest integer.

This problem is part of the set: Max and min.

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