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(n - 1)(m- 1)(x^{n+m} + y^{n+m}) + (n + m - 1)(x^ny^m + x^my^n) >= ...

Source: Austrian Polish 1995 APMC

April 26, 2020
inequalitiesalgebra

Problem Statement

Prove that for all positive integers n,mn,m and all real numbers x,y>0x, y > 0 the following inequality holds: (n−1)(m−1)(xn+m+yn+m)+(n+m−1)(xnym+xmyn)≥nm(xn+m−1y+xyn+m−1).(n - 1)(m- 1)(x^{n+m} + y^{n+m}) + (n + m - 1)(x^ny^m + x^my^n)\\ \\ \ge nm(x^{n+m-1}y + xy^{n+m-1}).
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