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JEE Main20198 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

The sum of the solutions of the equation x - 2 + x x - 4 + 2 = 0 , x > 0 is equal to

Options

  1. A10
  2. B9
  3. C12
  4. D4

Correct answer

A. 10

Step-by-step solution

Given, x - 2 + x x - 4 + 2 = 0 ⇒ x - 2 + x - 4 x + 2 = 0   ⇒ x - 2 + x 2 - 4 x + 4 = 2 (Adding 2 on both sides) ⇒ x - 2 2 + x - 2 = 2 ⇒ t 2 + t - 2 = 0   ; x - 2 = t   ;   t > 0 ⇒ t = 1 or t = - 2 ; Rejected because t > 0 ⇒ x - 2 = 1 ⇒ x = 3 or x = 1 ⇒ x = 9 or x = 1 Hence, the required sum = 10 .

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