Let s 7 ( x ) = 7 x 7 + a 6 x 6 + a 5 x 5 − 7 5 x 4 + 7 4 x 3 − 7 3 x 2 + 7 2 x − 7 . Find a 6 and a 5 such that x = − 7 1 is a rational root and the sum of the coefficients is 2 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) .
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