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COMEDK2015MathematicsTrigonometric Ratios & Identities

The number of solutions of the equation | x|= x+ 1 x ,(0 x 2 ) is

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

With the help of group of cot x , we know that When x (0, 2 ] ( , 3 2 ] , then x 0 | x|= x+ 1 x x= x+ 1 x 1 x =0 No solution exist. ...(i) When x ( 2 , ) ( 3 2 , 2 ) , then x < 0 aligned & &| x|= x+ 1 x &- x &= x+ 1 x &-2 x &= 1 x & & x= -1 2 x= 2 3 ...(ii) aligned From Eqs. (i) and (ii), only one solution exists.

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