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The number of real solutions of the equation x + 14 - 8 x - 2 + x + 23 - 10 x - 2 = 3 are

Options

  1. A2
  2. B4
  3. C8
  4. Dinfinite

Correct answer

A. 2

Step-by-step solution

The given equation is x - 2 - 4 2 + x - 2 - 5 2 = 3 ⇒ x - 2 - 4 + x - 2 - 5 = 3 Put x - 2 = y Then, the given equation becomes y - 4 + y - 5 = 3 Case 1 : y < 4 ⇒ - y + 4 - y + 5 = 3 ⇒ - 2 y = - 6 ⇒ y = 3 Case 2 : 4 ≤ y < 5 ⇒ y - 4 - y + 5 = 3 ⇒ 1 = 3 ⇒ no solution Case 3 : y ≥ 5 ⇒ y - 4 + y - 5 = 3 ⇒ 2 y = 12 ⇒ y = 6 y = 3 ⇒ x - 2 = 3 ⇒ x - 2 = 9 ⇒ x = 11 y = 6 ⇒ x - 2 = 6 ⇒ x - 2 = 36 ⇒ x = 38 ⇒ x = 11 and 38 i.e. two solutions.

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