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

Question

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

Navjyot Kalra · Answer

Sol. As x and y are positive real numbers and m and n are positive integers &there4; 1 + x 2n /2 &ge; (1 x x 2n ) 1/2 and 1 + y 2m /2 &ge; (1 x y 2m ) 1/2 { For two +ve numbers A. M. &ge; G. M.}

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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 y^m/(1 + x²ⁿ) (1 + y^2m) > 1/4

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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

1 Answers

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If x and y are positive real numbers and m, n are any positive integers, then xⁿ y^m/(1 + x²ⁿ) (1 + y^2m) > 1/4