Don't try x = y = z

Algebra Level 5

Let \(x, y, z\) be real numbers such that \(x^{2}+y^{2}+z^{2}=1\). Let the maximum possible value of \(\sqrt {6} xy+4yz\) be \(A\).Find \(A^{2}\).

This problem is inspired by Joel Tan.
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