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Geometry Level 3

f(x)=x2+121+x214x+218f(x) = \sqrt{x^{2} + 121} + \sqrt{x^{2} - 14x + 218}

Determine the value of xx that minimizes the function above.

If x=ab,x = \dfrac{a}{b}, where aa and bb are positive coprime integers, then find a+b.a + b.

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