Your destination for questions of the form "do we know if this expression is always greater than this other expression?" Explore what humans know about mathematical 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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