Let r and s be the roots of x^2 - 6x - 2 = 0. Find (r - s)^2.
(by Vieta's rules)
r+s = -6 <====== r^2 +2rs + s^2 = 36 r^2 + s^2 = 36-2rs
rs = -2 <======
(r-s)^2 = r^2 -2rs + s^2
r^2 + s^2 - 2rs
36-2rs - 2 rs
36 - -4 - -4 = 44
+36916 
