If A and B are the roots of x^2 - 4x + 1 = 0, then find A^3 + B^3.
This is simple. x^2-4x+1 is not factorable so we plug it into the quadratic equation.
x=−b±√b2−4ac2ax=4±√(−4)2−4(1)(1)2(1)x=4±√122x=4±2√32x=2±√3
Cube the two roots.
(2+√3)3+(2−√3)3=52