Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 - 6x + 1. Compute a^3 + b^3.
a^3 + b^3 = 56.
a^3 + b^3 = (a + b)((a + b)^2 - 3ab)
Use vieta's formulas!
x^2 - 2x + 6 = 0
a + b = 2
ab = 6
Plugging this in gives us
(2)(4 - 18) = -28.
