
Example: Solve, (x^{2} + 2x)^{2}  11(x^{2} + 2x) + 24 = 0 Solution: Put x^{2} + 2x = a in the given equation, we get a^{2}  11a + 24 = 0 a^{2}  11a + 24 = a^{2}  8a  3a + 24 = a(a  8)  3(a  8) = (a  8)(a  3) a = 3 or 8 Case (i) a = 3, x^{2} + 2x = 3 x^{2} + 2x  3 = 0 x^{2} + 3x  x  3 = 0 x(x + 3)  (x + 3) = 0 (x + 3)(x  1) x = 3 and 1 Case (ii) a = 8, x^{2} + 2x = 8 x^{2} + 2x  8 = 0 x^{2} + 4x  2x  8 = 0 x(x + 4)  2(x + 4) = 0 (x + 4)(x  2) = 0 x = 4 and 2 Therefore, the roots of the given equation are 3, 1, 4 and 2 Directions: Solve the following problems. Also write at least 5 examples of your own. 