Algebra
# Power Mean Inequalities

What is the minimum possible perimeter of a rectangle with area 25?

If $x^2 + y^2 = 1,$ find the maximum value of $(x + y)^2.$

Suppose $g(x)$ is positive for all $x$. Determine the minimum value of

$f(x) = \frac{16 (g(x))^2 + 1}{g(x)}.$