Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 - 14x + 2. Compute a^3/b^3 + b^3/a^3.
Simplify as
x^2 + 6x + 5 = 0
(x + 5) ( x + 1) = 0
x = -5 x = -1
Let a = -5 b = -1
a^3/b^3 + b^3 / a^3 =
(-5)^3 / ( -1)^3 + (-1)^3 / (-5)^3 =
125/1 + 1/125 =
125.008
+1725 
