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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


Team Careers360 12th Jan, 2024
Answer (1)
Team Careers360 15th Jan, 2024

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.

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