Algebra
# Classical Inequalities

What is the smallest possible value of the expression \[\frac{x^2+361}{x}\] for positive real \(x\)?

What is the minimum value of \[y=\frac{x^2}{x-9}\] when \(x>9\)?

How many ordered pairs of real numbers satisfy

\[ 36 ^ { x^2 + y} + 36 ^{ y^2 + x } = \frac{2} {\sqrt{6} } ? \]

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