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AP EAMCET20225 Jul 2022Morning ShiftMathematicsQuadratic EquationActual

4^x-3^ x- 1 2 =3^ x+ 1 2 -2^ 2 x-1 x=

Options

  1. A5 2
  2. B1 2
  3. C3 2
  4. D7 2

Correct answer

C. 3 2

Step-by-step solution

Given, 4^x-3^ x- 1 2 =3^ x+ 1 2 -2^ 2 x-1 aligned & (2)^ 2 x +2^ 2 x-1 =3^ x+ 1 2 +3^ x- 1 2 & 2^ 2 x + 2^ 2 x 2 =3^x 3 + 3^x 3 & 2^ 2 x [1+ 1 2 ]=3^x [ 3 + 1 3 ] aligned aligned & 2^ 2 x 3 2 =3^x 4 3 & 2^ 2 x (3 3 )=3^x(8) & 2^ 2 x (3)^ 3 2 =3^x (2)^3 aligned Comparing power of 2,2 x=3 and comparing power of 3, x= 3 2 Both equations given us x= 3 2 .

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