Problem 17

Algebra Level 3

\[\sqrt { { 8x }^{ 2 }-12x-39 } +\sqrt { { 2x }^{ 2 }-3x-15 } -\sqrt { { 2x }^{ 2 }-3x+20 } =0\]

Solve the equation, the roots of the above equation can be represented as \(\frac { A\pm \sqrt { B } }{ 4 } ,\text{gcd}(A,B)=1\).

Find the value of \(A+B\).

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