Let $x,$ $y,$ $z$ be positive real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[xy \sqrt{10} + yz.\]
Question:
Let $x,$ $y,$ $z$ be positive real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[xy \sqrt{10} + yz.\]
Answer:
Let's think step by step.

user
\frac{\sqrt{11}}{2}
Let $x,$ $y,$ $z$ be positive real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[xy \sqrt{10} + yz.\]
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