Seems like Cauchy

Algebra 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 \( \sqrt{ \dfrac{m}{n}} \), where \(m\) and \(n\) are coprime positive integers. Find \( m+n \).

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