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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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