Question
Solution of 2^x+2^ |x| 2 2 is
BITSAT
Mathematics
Quadratic Equation
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Mathematics Question (2023) — Solution
Options
- A. (- , _2( 2 +1) )
- B. (0, )
- C. ( 1 2 , _2( 2 -1) )
- D. (- , _2( 2 -1) ] [ 1 2 , )
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 , )
Related: Mathematics — Quadratic Equation · All PYQ Banks