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BITSAT2023MathematicsQuadratic EquationActual

Solution of 2^x+2^ |x| 2 2 is

Options

  1. A(- , ₂( 2 +1) )
  2. B(0, )
  3. C( 1 2 , ₂( 2 -1) )
  4. D(- , ₂( 2 -1) ] [ 1 2 , )

Correct answer

D. (- , ₂( 2 -1) ] [ 1 2 , )

Step-by-step solution

2^x+2^ |x| 2 2 ...(i) Case I: x 0 , then Eq. (i) becomes 2^x+2^x 2 2 2^x 2 x 1 2 Case II: x 2^x+2^ -x 2 2 t+ 1 t 2 2 , where 2^x=t t^2-2 2 t+1 0 x ₂( 2 -1) Also, 0 The solution is . (- , ₂( 2 -1) ) ] [ 1 2 , )

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