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Which of the following set of values of x satisfies the equation 2^ (2 ^2 x-3 x+1 ) +2^ (2-2 ^2 x+3 x ) =9 ?

Options

  1. Ax = n 6 , n I
  2. Bx = n 3 , n I
  3. Cx = n , n I
  4. Dx =2 n + 2 , n I

Correct answer

D. x =2 n + 2 , n I

Step-by-step solution

aligned & 2^ (2 ^2 x-3 x+1 ) +2^ 3- (2 ^2 x-3 x+1 ) =9 & 2^ 2 ^2 x-3 x+1 =t & t+ 8 t =9 t^2-9 t+8=0 & (t-8)(t-1)=0 & 2 ^2 x-3 x+1=3 & or 2 ^2 x-3 x+1=0 & x=- 1 2 , x= 1 2 , x=1 aligned

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