Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^2 b + b^3 = -679. Find a + b.
+2221
Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^2 b + b^3 = -679. Find a + b.
a3 + 3ab2 = 679
3a2b + b3 = –679
add them to get a3 + 3ab2 + 3ba2 + b3 = 0
this factors to (a + b)3 = 0
a + b = 0
Verified this by plotting (a+b)3 = 0 on Desmos.
The curve is identical to the curve for y = –x.
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