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AP EAMCET20224 Jul 2022Morning ShiftMathematicsQuadratic EquationActual

The number of real roots of the equation x 1 - x + 1 - x x = 13 6 is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

Given x 1 - x + 1 - x x = 13 6 Let t = x 1 - x i.e. x 1 - x > 0   &   x ≠ 0 , 1 i.e. x 1 - x > 0 ⇒ x x - 1 < 0 ⇒ x ∈ 0 , 1 Now, t + 1 t = 13 6 ⇒ 6 t 2 - 13 t + 6 = 0 ⇒ t = 13 ± 169 - 144 12 = 3 2 ,   2 3 i.e. when x 1 - x = 3 2 ⇒ x 1 - x = 9 4 ⇒ 4 x = 9 - 9 x ⇒ x = 9 13 when x 1 - x = 2 3 ⇒ x 1 - x = 4 9 ⇒ 9 x = 4 - 4 x ⇒ x = 4 13 Hence, there are two real roots.

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