Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 4x + 5. Compute (a - 4b)(b - 4a).
Simplify as
x^2 + 5x - 10 = 0
ab = -10
a + b = -5 square both sides
a^2 + 2ab + b^2 = 25
a^2 + b^2 + 2(-10) = 25
a^2 + b^2 = 45
(a - 4b) ( b -4a) =
ab - 4b^2 - 4a^2 + 16ab =
17ab - 4 ( a^2 + b^2)
17 (-10) - 4 (45) =
-170 - 180 =
-350
+1765 
