An inequality for the powers of triangle sides

Abstract. An inequality will be presented for areas of triangles with side lengths given by the powers of a given triple. For small powers we provide separate proofs, for some further cases computer aided proofs are proposed. Finally we prove our statement in full.

Key words and phrases. Heron's formula, Ono's and Weitzenböck's inequality, Schur's and Muirhead's inequality, majorization.