It is as tough as it looks

Calculus Level 4

Let A=9+x23x2+16+x24x2{A=\sqrt { 9+x^{ 2 }-3x\sqrt { 2 } } +\sqrt { 16+x^{ 2 }-4x\sqrt { 2 } }} .

The value of x x ^* such that ddxA=0{\frac { d }{ dx } A=0} can be expressed as x=abc.x^* = \frac { a\sqrt { b } }{ c }. Then find a+b+c a + b + c .

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