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MHT CET20239 May 2023Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The number of solutions in [0,2 ] of the equation 16^ ^2 x +16^ ^2 x =10 is

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

D. 8

Step-by-step solution

aligned & 16^ ^2 x +16^ ^2 x =10 & 16^ ^2 x +16^ 1- ^2 x =10 & 16^ ^2 x + 16 16^ ^2 x =10 aligned Let 16^ ^2 x = t array ll & t + 16 t =10 & t ^2-10 t +16=0 & t =2 and t =8 array Now, 16^ ^2 x =2 and 16^ ^2 x =8 aligned & 2^ 4 ^2 x =2^1 and 2^ 4 ^2 x =2^3 & 4 ^2 x=1 and 4 ^2 x=3 & ^2 x= 1 4 and ^2 x= 3 4 & x= 1 2 and x= 3 2 & x= 6 , 5 6 , 7 6 , 11 6 and x= 3 , 2 3 , 4 3 , 5 3 aligned number of solutions =8 .

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