AP EAMCET20224 Jul 2022Evening ShiftMathematicsQuadratic EquationActual
The sum of all the real roots of the equation x - 2 2 + x - 2 - 2 = 0 is
Options
- A7
- B4
- C1
- DNone of these
Correct answer
B. 4
Step-by-step solution
Given: x - 2 2 + x - 2 - 2 = 0       . . . . 1 Putting y = x - 2 , then we can rewrite 1 as y 2 + y - 2 = 0 ⇒ y 2 + 2 y - y - 2 = 0 ⇒ y y + 2 - y + 2 = 0 ⇒ y - 1 y + 2 = 0 ⇒ y = 1 ,   - 2 Since, y ≥ 0 , so y = x - 2 = 1 ⇒ x - 2 = ±   1 ⇒ x = 3   o r   1 Required sum is = 3 + 1 = 4