A) \[-2-\sqrt{3}<x<-2+\sqrt{3}\]
B) \[2-\sqrt{3}<x<7+\sqrt{3}\]
C) \[2-\sqrt{3}<x<2+\sqrt{3}\]
D) None of the above
Correct Answer: A
Solution :
\[\because \] \[\left| x+\frac{1}{x} \right|<4\] \[\Rightarrow \] \[\frac{{{x}^{2}}+1}{|x|}<4\] \[\Rightarrow \] \[|x{{|}^{2}}-\,\,4|x|+1<0\] \[\Rightarrow \] \[{{(|x|-2)}^{2}}<3\] \[\Rightarrow \] \[{{(|x|-2)}^{2}}<{{(\sqrt{3})}^{2}}\] \[\Rightarrow \] \[||x|-2<\sqrt{3}\] \[\Rightarrow \] \[-\sqrt{3}<(|x|-2)<3\] \[\Rightarrow \] \[2-\sqrt{3}<x<2+\sqrt{3}\] When\[x>0,\,\,2-\sqrt{3}<x<2+\sqrt{3}\] and when\[x<0,\,\,-2-\sqrt{3}<x<-2+\sqrt{3}\]
You need to login to perform this action.
You will be redirected in
3 sec
