Algebra or Calculus?

Algebra Level 4

Let x,yx,y and zz be real numbers satisfying 5x+6y+7z=85x+6y+7z=8, find the minimum value of x2+y2+z2x^2+y^2+z^2.

If your answer is of the form AB \dfrac AB, where AA and BB are coprime positive integers, submit A+BA+B.

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