Algebraic/Geometric Manipulations

Geometry Level 4

\[\displaystyle{{ x }+{ y }={ \left( \cfrac { \sqrt { x } }{ \sqrt { y } } +\cfrac { \sqrt { y } }{ \sqrt { x } } \right) }^{ 2 }}\]

\(x\) and \(y\) are positive real numbers satisfying the above equation.

Find Maximum value of \[\displaystyle{\cfrac { 24\sqrt { x } +7\sqrt { y } +31\sqrt { xy } }{ \sqrt { xy } } }\]

Credits:

Megh choksi
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