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KVPY2014MathematicsTrigonometric Equations

The number of solutions to the equation ⁴ x+ 1 ² x = ⁴ x+ 1 ² x in the interval [0,2 ] is :

Options

  1. A6
  2. B4
  3. C2
  4. D0

Correct answer

B. 4

Step-by-step solution

⁴ x- ⁴ x= 1 ² x - 1 ² x ( ² x- ² x )= ( ² x- ² x ) ² x ² x 2 x= 4 2 x ² 2 x 2 x (1-4 cosec ² 2 x )=0 2 x=02 x=2 n 2 x=n 4 At n=0, x= 4 n=1 ; x= 5 4 , 3 4 n=2, x= 7 4

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