A) \[\frac{m+n}{6mn}\]
B) 1
C) 1/2
D) ¼
Correct Answer: D
Solution :
Here, \[\frac{{{x}^{m}}{{y}^{n}}}{(1+{{x}^{2m}})(1+{{y}^{2n}})}=\frac{1}{\left( {{x}^{m}}+\frac{1}{{{x}^{m}}} \right)\left( {{x}^{n}}+\frac{1}{{{x}^{n}}} \right)}\] Now,\[{{x}^{m}}+\frac{1}{{{x}^{m}}}\ge 2\]and\[{{y}^{n}}+\frac{1}{{{y}^{n}}}\ge 2\] \[\therefore \]\[\frac{1}{\left( {{x}^{m}}+\frac{1}{{{x}^{m}}} \right)\left( {{y}^{n}}+\frac{1}{{{y}^{n}}} \right)}\le \frac{1}{4}\]
You need to login to perform this action.
You will be redirected in
3 sec
