Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^2 b + b^3 = -652. Find a+b.
Thank you!
algebraic solver => a = 7.44856, b = -3.44856, so a + b = 4.
a^3 + 3ab^2 = 679
3a^2b + b^3 = -652
Note that ( a + b)^3 = ( a^3 + 3a^2b) + (3ab^2 + b^2) = (a^3 + 3ab^2 ) + ( 3a^2b + b^3)
So
( a + b)^3 = 679 - 652
(a + b)^3 = 27 take the cube root of both sides
(a + b) = 3
