Question
Number of real solution of 5- _2|x| =3- _2|x| is equal to
BITSAT
Mathematics
Functions
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 1
- B. 2
- C. 3
- D. 4
Answer
B. 2
Step-by-step solution
aligned & Let & _2|x| & =t (i)\\ & & 5-t & =3-t \\ & & 5-t & =(3-t)^2 \\ & & 5-t & =9+t^2-6 t aligned aligned & t^2-5 t+4=0 \\ & (t-4)(t-1)=0 \\ & t=1 or 4 [rejected] \\ & [ 5-4 =3-4,1 -1] \\ & _2|x|=1 \\ & |x|=2 \\ & x= 2 aligned Total 2 real solutions.
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