The number of real roots of the equation x 2 - 4 x + 3 + x 2 - 9 = 4 x 2 - 14 x + 6 , is:

Step-by-step solution

Given, x 2 - 4 x + 3 + x 2 - 9 = 4 x 2 - 14 x + 6 ⇒ x - 3 x - 1 + x - 3 x + 3 = x - 3 4 x - 2 ⇒ x - 3 x - 1 + x - 3 x + 3 - x - 3 4 x - 2 = 0 ⇒ x - 3 = 0   or  x - 1 + x + 3 - 4 x - 2 = 0 So, x = 3 is one solution and also x ≥ 3 Now solving x - 1 + x + 3 - 4 x - 2 = 0 ⇒ x - 1 + x + 3 = 4 x - 2 Now squaring both side we get, ⇒ x - 1 + x + 3 + 2 x - 1 x + 3 = 4 x - 2 ⇒ 2 x - 1 x + 3 = 2 x - 4 ⇒ x - 1 x + 3 = x - 2 2 ⇒ x 2 + 2 x - 3 = x 2 - 4 x + 4 &#8658