Problem 17

Algebra Level 3

8x212x39+2x23x152x23x+20=0\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 A±B4,gcd(A,B)=1\frac { A\pm \sqrt { B } }{ 4 } ,\text{gcd}(A,B)=1.

Find the value of A+BA+B.

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