Determine the set of all real x satisfying (x^2+3x-1)^2<9
Enter your answer in interval notation.
Take both roots and we have that
x^2 + 3x - 1 = 3 x^2 + 3x - 1 = - 3
x^2 + 3x - 4 = 0 x^2 + 3x + 2 = 0
(x + 4) (x - 1) = 0 (x + 2) ( x + 1) = 0
Setting each factor to 0 and solving for x gives the answers that x = { -4, - 2,- 1, 1 }
So....we have the possible answers
(-inf, -4) ( -4, -2) ( -2, -1) (-1, 1) or ( 1 inf )
Testing a point in each interval in the original inequality we see that the solution intervals are
(-4, -2) U (-1, 1)