Algebraic/Geometric Manipulations

Geometry Level 4

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

xx and yy are positive real numbers satisfying the above equation.

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

Credits:

Megh choksi
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