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 \(\frac{M}{m}\).

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