Equations And Inequalities Question 6
Question: If $ | \frac{12x}{4x^{2}+9} |\ge 1 $ for all real values of $ x, $ the inequality being satisfied only if $ | x | $ is equal to
Options:
A) $ \frac{3}{2} $
B) $ \frac{2}{3} $
C) $ \frac{1}{3} $
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ | \frac{12x}{4x^{2}+9} |\ge 1\Rightarrow \frac{12| x |}{4x^{2}+9}\ge 1 $ $ \because 4x^{2}+9>0 $
$ \Rightarrow 4x^{2}-12| x |+9\le 0 $
$ \Rightarrow 4{{| x |}^{2}}-12| x |+9\le 0 $
$ \Rightarrow {{(2| x |-3)}^{2}}=0\Rightarrow | x |=\frac{3}{2} $
BETA
