The sum of the real roots of the equation x - 6 - 1 2 - 3 x x - 3 - 3 2 x x + 2 = 0 , is equal to:

Step-by-step solution

Given x - 6 - 1 2 - 3 x x - 3 - 3 2 x x + 2 = 0 On expansion, we get x - 3 x x + 2 - 2 x x - 3 + 6 2 x + 2 + 3 x - 3 - 1 4 x - 9 x = 0 ⇒ x - 3 x 2 - 6 x - 2 x 2 + 6 x + 6 2 x + 4 + 3 x - 9 - 1 - 5 x = 0 ⇒ - 5 x 3 + 30 x - 30 + 5 x = 0 ⇒ 5 x 3 - 35 x + 30 = 0 ⇒ x 3 - 7 x + 6 = 0 ⇒ x - 1 x - 2 x + 3 ⇒ x = 1 or x = 2 or x = - 3 . Here all roots 1 ,   2 ,   - 3 are real, hence the sum of the real roots is 1 + 2 - 3 = 0 .