It is as tough as it looks

Calculus Level 5

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

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

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