Let A = x R : |x^2 - 5x + 5| < 1 and B = x R : x - 2 x - 4 0 . Then A B is equal to

Step-by-step solution

For set A , we have the inequality |x^2 - 5x + 5| This is equivalent to -1 1) x^2 - 5x + 5 > -1 x^2 - 5x + 6 > 0 (x - 2)(x - 3) > 0 x (- , 2) (3, ) 2) x^2 - 5x + 5 x (1, 4) Taking the intersection of these two conditions, we get set A : A = (1, 2) (3, 4) For set B , we have the rational inequality x - 2 x - 4 0 . The critical points are x = 2 and x = 4 . Since the denominator cannot be zero, x 4 . Using the wavy curve method, the solution is: B = [2, 4) Now, we find the intersection A B : A B = ((1, 2) (3, 4)) [2,