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 :
${1 \over 2}$
${1 \over 4}$
${{m + n} \over {6mn}}$
1
Solution
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