+0  
 
0
216
1
avatar

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
 #1
avatar+9466 
+1

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

 

Adding gives 

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

 

So a + b = 0.

 May 2, 2022

5 Online Users

avatar
avatar