Problem #PRU-57480-3

Problems Geometry Plane geometry Geometrical inequalities Inequalities in a triangle A perpendicular distance is the shortest. Inequalities for right triangles
 13–13  2.0

Problem

\(ABC\) is a right angled triangle with a right angle at \(C\). Prove that \(c^n > a^n + b^n\) for \(n > 2\).