Question : If $\left (x+\frac{1}{x}\right )=5$, find the value of $\frac{6x}{x^{2}+x+1}$.
Option 1: 3
Option 2: 2
Option 3: 1
Option 4: 0
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Correct Answer: 1
Solution :
Given: $\left (x+\frac{1}{x} \right)=5$
⇒ $\frac{x^2+1}{x}=5$
⇒ $x^2+1=5x$
Adding $x$ on both sides,
⇒ $x^2+1+x=5x+x$
⇒ $x^2+x+1=6x$
Now, put the value of $x^2+x+1=6x$ in the expression $\frac{6x}{x^{2}+x+1}$
So, $\frac{6x}{x^{2}+x+1}=\frac{6x}{6x}=1$
Hence, the correct answer is 1.
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