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Paragraph: In reducing a given equation to the standard forms ( x= etc ) we apply several trigonometric or algebraic transformations. As a result of which the canonical form finally obtained may not be equivalent to the original equation resulting either in loss of solutions or in the appearance of fake solutions The equation 2 2 x-3 3 x= 2 x has

Options

  1. Atwo solutions in (0, 3 )
  2. Bone solution in (0, 3 )
  3. Cno solution in (- , )
  4. Dnone of these

Correct answer

C. no solution in (- , )

Step-by-step solution

2 2 x 2 x -3 3 x 3 x = 2 x 2 x 2 (2 ^2 x-1 ) 2 x x -3 4 ^3 x-3 x 3 x-4 ^3 x = 2 x x 2 ^2 x-1 Now Let ^2 x = t in above i.e. t (0,1)- 1 2 Now we have 2 t-1-3 t 4 t-3 4 t-1 = 2 t(1-t) 2 t-1 Solving t = 1 but t (0,1)- 1 2 So there is no t , so there is no x

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