# More fun in 2015, Part 28

Algebra Level 5

$5x^2+6y^2+7z^2=4xy+4yz+2015$

Let $$M$$ and $$m$$ be the maximum and the minimum of $$x^2+y^2+z^2$$ subject to the constraint above, where $$x,y$$ and $$z$$ are real numbers. Find $$\frac{M}{m}$$.

×