MathDB

9

Part of 1995 Austrian-Polish Competition

Problems(1)

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

Source: Austrian Polish 1995 APMC

4/26/2020
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}).
inequalitiesalgebra