Algebra
# Power Mean 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

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