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))) lt 1/4`

If `x and y` are positive real numbers and `m, n` are any positive int

1.	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))) lt 1/4`
Answer» Correct Answer - 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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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))) lt 1/4`

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