# 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 $$A+B$$.

×