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If x and y are positive real numbers an...

If `x and y` are positive real numbers and `m, n` are any positive integers, then Prove that `(x^n y^m)/((1+x^(2n))(1+y^(2m))) lt =1/4`

Text Solution

Verified by Experts

The correct Answer is:
False
Using `AM ge GM`,
`(1 + x^(2n))/(2) ge sqrt(1.x^(2n))`
`rArr (1 + x^(2n))/(2) ge x^(n)`
`rArr (x^(n))/(1 + x^(2n)) le (1)/(2)`
`:. (x^(n).y^(m))/((1 + x^(2n)) (1 + y^(2m))) le (1)/(4)`
Hence, it is false statement
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