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
by
Karan Shekhawat