Let x , y be positive real numbers and m , n positive integers. The maximum value of the expression ( 1 + x 2 m ) ( 1 + y 2 n ) x m y n is :

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Let x , y be positive real numbers and m , n positive integers. The maximum value of the expression ( 1 + x 2 m ) ( 1 + y 2 n ) x m y n ​ is :

TestHub · Accepted Answer

A = ( 1 + x 2 m ) ( 1 + y 2 n ) x m y n ​ = ( x − m + x m ) ( y − n + y n ) 1 ​ 2 x m + y − m ​ ≥ ( x n + 1 , x − m ) 2 1 ​ ⇒ x n + + x − n ≥ 2 In the same way, y n + y n ≥ 2 Then , ( x n + x − n ) ( y − n + y n ) ≥ 4 ⇒ ( x "1 + x − m ) ( y − n + y n ) 1 ​ ≤ 4 1 ​

Mathematics - Application of Derivative Question with Solution | TestHub

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