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1984

JEE Main 1984 Mathematics question on Complex Numbers and Quadratic Equations

The equation x−2x−1=1−2x−1x - \dfrac{2}{x-1} = 1 - \dfrac{2}{x-1} has
  1. A.
    no root
  2. B.
    one root
  3. C.
    two equal roots
  4. D.
    infinitely many roots
Show answer and solution

Correct option: A

Solution

Rearranging: x - 2/(x-1) = 1 - 2/(x-1). The term -2/(x-1) appears on both sides, so cancel it to get x = 1. But x = 1 makes the denominator (x-1) = 0, which is undefined. So x = 1 is an extraneous solution and the equation has no valid root.

[1984]

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