Sum of possible sums multiplied by 625

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a and b are real numbers that satisfies the equation a 3 + b 3 + 3 a b = 1 a^3 + b^3 + 3ab = 1 . Let N N be the sum of all possible values of a + b a + b . What is the value of 625 N 2 625N^2 ?


The answer is 625.

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