Find the solution set

Find the solution set Find the solution set of inequation (x2 —x— 1) (x2 — x— 7) < —5

(x^{2} - x - 1) (x^{2} - x - 7) < - 5 L e t x^{2} - x = t (t - 1) (t - 7) < - 5 t^{2} - t - 7 t + 7 < - 5 t^{2} - 8 t + 12 < 0 t^{2} - 6 t - 2 t + 12 < 0 t (t - 6) - 2 (t - 6) < 0 (t - 6) (t - 2) < 0 S o l u t i o n o f e q u a t i o n (x - a) (x - b) < 0, w h e r e a < b, i s g i v e n b y x \in (a, b) t \in (2, 6) 2 < x^{2} - x < 6 f i r s t c o n s i d e r x^{2} - x > 2 x^{2} - x - 2 > 0 x^{2} - 2 x + x - 2 > 0 x (x - 2) + (x - 2) > 0 (x - 2) (x + 1) > 0 (x - 2) (x - (- 1)) > 0 S o l u t i o n o f e q u a t i o n (x - a) (x - b) > 0, w h e r e a < b, i s g i v e n b y x \in (- \infty, a) \cup (b, \infty) x \in (- \infty, - 1) \cup (2, \infty) N o w c o n s i d e r x^{2} - x < 6 x^{2} - x - 6 < 0 x^{2} - 3 x + 2 x - 6 < 0 x (x - 3) + 2 (x - 3) < 0 (x - 3) (x + 2) < 0 (x - (- 2)) (x - 3) < 0 S o l u t i o n o f e q u a t i o n (x - a) (x - b) < 0, w h e r e a < b, i s g i v e n b y x \in (a, b) x \in (- 2, 3) B u t x \in (- \infty, - 1) \cup (2, \infty) T a k i n g i n t e r s e c t i o n w e h a v e x \in (- 2, - 1) \cup (2, 3)