JEE Main20208 Jan 2020Evening ShiftMathematicsQuadratic EquationActual

Let S , be the set of all real roots of the equation, 3 x 3 x - 1 + 2 = 3 x - 1 + 3 x - 2 , then

Options

Acontains exactly two elements.
Bis a singleton.
Cis an empty set.
Dcontains at least four elements.

Correct answer

B. is a singleton.

Step-by-step solution

Let 3 x = t t t - 1 + 2 = t - 1 + t - 2 t 2 - t + 2 = t - 1 + t - 2 Let, f t = t 2 - t + 2   &   g t = t - 1 + t - 2 f t   &   g t has a solution at t = a . 3 x = a   ⇒ x = log 3 ⁡ a . So, it is a singleton set.

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