Let x, y be positive real numbers and m...

Let x, y be positive real numbers and m, n be positive integers, The maximum value of the expression
`(x^(m)y^(n))/((1+x^(2m))(1+y^(2n)))` is

A

`(m+ n)/(6mn)`

B

1

C

`(1)/(2)`

D

`(1)/(4)`

Verified by Experts

The correct Answer is:

D

Similar Questions

Explore conceptually related problems

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

If x^(m)y^(n)=(x+y)^(m+n)

If are positive integers, maximum value of x^(m) (a-x)^(n)" in (0,a) is :"

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)

Let x and y be two positive real numbers such that x + y = 1. Then the minimum value of 1/x+1/y is-

If x,y is positive real numbers then maximum value of (x^(m)y^(m))/((1+x^(2m))(1+y^(2n))) is (A)(1)/(4)(B)(1)/(2) (C) (m+n)/(6mn) (D) 1

Let x and y be two positive real numbers such that x+y= 1 . Then the minimum value of (1)/(x) + (1)/(y) is