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If x and y are positive real numbers and m, n are any positive integers, then x n y m /(1 + x 2n ) (1 + y 2m ) > 1/4

 If x and y are positive real numbers and m, n are any positive integers, then xn ym/(1 + x2n) (1 + y2m) > 1/4

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Sol. As x and y are positive real numbers and m and n are positive integers
∴ 1 + x2n/2 ≥ (1 x x2n)1/2 and 1 + y2m/2 ≥ (1 x y2m)1/2
{ For two +ve numbers A. M. ≥ G. M.}

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