QJEEM19Maf127: JEE Main 2019 Mathematics - Class 11 JEEM19Maf127 Solution: Let x, y be positive real numbers and m, n positive integers.…

Question

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Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression

{{{x^m}{y^n}} \over {\left( {1 + {x^{2m}}} \right)\left( {1 + {y^{2n}}} \right)}}

is :

Accepted Answer

{{{x^m}{y^n}} \over {\left( {1 + {x^{2m}}} \right)\left( {1 + {y^{2n}}} \right)}} = {1 \over {\left( {{x^m} + {1 \over {{x^m}}}} \right)\left( {{y^n} + {1 \over {{y^n}}}} \right)}} \le {1 \over 4}

using AM

\ge

GM

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