Multivariable Function
As and range over the positive real numbers, the maximum value of can be expressed as , where and are relatively prime positive integers. Find .
The answer is 5121.
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1 solution
Surely,a straightforward application of AM-GM inequality on the expressions in the given parenthesis will not work because it will give a upper bound but not the supremum (the sharpest upper bound) .Hence we need to rearrange the terms sothat we get a solution set (x,y,z) for which the maxima is attained.