Algebra or Calculus?

Algebra Level 4

Let \(x,y\) and \(z\) be real numbers satisfying \(5x+6y+7z=8\), find the minimum value of \(x^2+y^2+z^2\).

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

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