The number of real solutions of the equation 3 x 2 + 1 x 2 - 2 x + 1 x + 5 = 0 , is

Step-by-step solution

Given equation is: 3 x 2 + 1 x 2 - 2 x + 1 x + 5 = 0 We know, x + 1 x 2 = x 2 +   2 + 1 x 2       ( using algebraic identities ) ⇒ x 2 + 1 x 2 = x + 1 x 2 - 2 So, we can write the given equation as 3 x + 1 x 2 - 2 - 2 x + 1 x + 5 = 0 Let x + 1 x = t ⇒ 3 t 2 - 2 - 2 t + 5 = 0 ⇒ 3 t 2 - 6 - 2 t + 5 = 0 ⇒ 3 t 2 - 2 t - 1 = 0 ⇒ 3 t 2 - 3 t + t - 1 = 0 ⇒ 3 t t - 1 + ( t - 1 ) = 0 ⇒ 3 t + 1 t - 1 = 0 Therefore, t = - 1 3   or   t = 1 Case &