+1725 Let a and b be the roots of 5x^2 - 11x + 4 = -3x^2 - 17x + 5. Find a^3 + b3.
+129771 Simplify as
8x^2 + 6x - 1
ab = -1/8
2ab = (-1/4)
a + b = -6/8 = -3/4 square both sides
a^2 + b^2 + 2ab = -9/16
a^2 + b^2 -1/4 = -9/16
a^2 + b^2 = -9/16 + 1/4 = -5/16
a^3 + b^3 = (a + b) ( a^2 + b^2 - ab) =
(-3/4) ( -5/16 - (-1/8)) =
(-3/4) ( -5/16 + 1/8) =
(-3/4) ( -3/16) =
9 / 64
