Let a and b be complex numbers. If a + b = 4 and a^2 + b^2 = 6 + ab, then what is a^3 + b^3?

onyuIee Jul 30, 2024

#1**+1 **

We can use a series of equations to solve this problem.

First, let's focus on what we are trying to compute, a^3+b^3.

Now, note that

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

Wait! We already have all the terms needed to solve this problem. We have

\(a^3+b^3=4(6+ab - ab) = 4(6) = 24\)

Thus, our answer is just 24.

Thanks! :)

NotThatSmart Jul 30, 2024