(x^2+x-6)(x^2-3x-4)=24

(x^2+x-6)(x^2-3x-4)=24 Hint. L.H.S. = 10. (x 2 + x — 6) (x 2 — 3 x — 4) = 24. Hint. L.H.S. = (x + 3) (x - 3 2 II-x x 13 6

Dear student

(x^{2} + x - 6) (x^{2} - 3 x - 4) = 24 (x^{2} + 3 x - 2 x - 6) (x^{2} - 4 x + x - 4) = 24 [x (x + 3) - 2 (x + 3)] [x (x - 4) + 1 (x - 4)] = 24 (x - 2) (x + 3) (x + 1) (x - 4) = 24 (x - 2) (x + 3) (x + 1) (x - 4) - 24 = 0 (x + 3) (x - 4) (x - 2) (x + 1) - 24 = 0 (x^{2} - x - 12) (x^{2} - x - 2) - 24 = 0 Let x^{2} - x = u (u - 12) (u - 2) - 24 = 0 u^{2} - 2 u - 12 u + 24 - 24 = 0 u^{2} - 14 u = 0 u (u - 14) = 0 u = 0, u = 14 Now, x^{2} - x = 0 x (x - 1) = 0 x = 0 and x = 1 and x^{2} - x = 14 x^{2} - x - 14 = 0 x = \frac{1 \pm \sqrt{1 + 56}}{2} x = \frac{1 \pm \sqrt{57}}{2} So, x = 0, 1, \frac{1 \pm \sqrt{57}}{2}

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