Question : If $\frac{x^{2}-x+1}{x^{2}+x+1}=\frac{2}{3}$, then the value of $\left (x+\frac{1}{x} \right)$ is:
Option 1: 4
Option 2: 5
Option 3: 6
Option 4: 8
Correct Answer: 5
Solution :
Let $( x+\frac{1}{x})$ be $y$.
$\frac{x^{2}-x+1}{x^{2}+x+1}=\frac{2}{3}$
Taking $x$ common in both numerator and denominator, we get,
$⇒\frac{x( x+\frac{1}{x}-1)}{x( x+\frac{1}{x}+1)}=\frac{2}{3}$
$⇒\frac{y-1}{y+1}=\frac{2}{3}$
$⇒3y-3=2y+2$
$\therefore y = x+\frac{1}{x} = 5$
Hence, the correct answer is 5.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
