# Seems like Cauchy

Number Theory Level 4

The maximum value of $$f(x,y,z) = 5x+4y+4z$$ on the ellipsoid $$10x^2 + 20y^2 + 15z^2 = 1$$ can be expressed in the form $$\sqrt{ \frac{m}{n}}$$. Find $$m+n$$.

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