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MHT CET202613 April 2026Morning ShiftMathematicsTrigonometric EquationsActual

The number of solutions in [0, 2 ) of the equation 3x 5x = 7x is

Options

  1. A4
  2. B5
  3. C7
  4. D6

Correct answer

D. 6

Step-by-step solution

Given equation: 3x 5x = 7x 3x 5x 5x = 7x 2 5x 3x = 2 7x 5x Using the identity 2 A B = (A+B) + (A-B) : 8x + 2x = 12x + 2x 12x - 8x = 0 Using the identity C - D = 2 ( C-D 2 ) ( C+D 2 ) : 2 2x 10x = 0 This gives 2x = 0 or 10x = 0 . For 2x = 0 , 2x = n x = n 2 . Since x [0, 2 ) , the only solution is x = 0 . For 10x = 0 , 10x = (2k+1) 2 x = (2k+1) 20 . Since x [0, 2 ) , we have 0 (2k+1) 20 The possible values for 2k+1 are 1, 3, 5, 7, 9 . This gives x = 20 , 3 20 , 5 20 , 7 20 , 9 20 . We must also ensure that 5x is def

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