# It is as tough as it looks

Calculus Level 4

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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