BITSAT2023MathematicsQuadratic EquationActual
Solution of 2^x+2^ |x| 2 2 is
Options
- A(- , ₂( 2 +1) )
- B(0, )
- C( 1 2 , ₂( 2 -1) )
- 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 , )