Don't try x = y = z

Algebra Level 4

Let x,y,zx, y, z be real numbers such that x2+y2+z2=1x^{2}+y^{2}+z^{2}=1. Let the maximum possible value of 6xy+4yz\sqrt {6} xy+4yz be AA.Find A2A^{2}.

This problem is inspired by Joel Tan.
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