Complex Numbers And Quadratic Equations question 738
Question: If $ |x-2|+|x-3|=7 $ , then x =
Options:
A) 6
B) -1
C) 6 or -1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Here $ x=2 $ and 3 are the critical points. When $ x<2,|x-2|=-(x-2),|x-3|=-(x-3) $
$ \therefore $ The given equation reduces to $ 2-x+3-x=7 $
Þ $ x=-1<2 $ \ $ x=-1 $ is a solution. When $ 2\le x<3,|x-2|=x-2,|x-3|=-(x-3) $ \ The equation reduces to $ x-2+3-x=7 $
Þ 1=7 \ No solution in this case. When $ x\ge 3 $ , the equation reduces to $ x-2+x-3=7 $
Þ $ x=6>3 $ Hence we get, $ x=6 $ or -1 Trick: By inspection, we have that both the values $ x=6,-1 $ satisfy the given equation.
BETA
