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Symmetric Matrices & Quadratic Forms · Medium problem

On the unit sphere x2+y2+z2=1x^2 + y^2 + z^2 = 1, let MM and mm be the maximum and minimum of q(x,y,z)=3x2+2y2−z2+4yzq(x, y, z) = 3x^2 + 2y^2 - z^2 + 4yz. Find M−mM - m.