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Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^2 b + b^3 = -679. Find a + b.

 May 2, 2022
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\(\begin{cases}a^3 + 3ab^2 = 679\\3a^2 b + b^3 = -679\end{cases}\)

 

Adding gives 

\(a^3 + 3a^2 b + 3ab^2 + b^3 = 0\\ (a + b)^3 = 0\)

 

So a + b = 0.

 May 2, 2022

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