Question : The sum of twice a fraction and its reciprocal is $\frac{17}{6}$. What is the fraction?
Option 1: $\frac{4}{3}$
Option 2: $\frac{5}{4}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{4}{5}$
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Correct Answer: $\frac{3}{4}$
Solution :
Let's assume the fraction is $x$.
$⇒2x+\frac{1}{x}=\frac{17}{6}$
Multiplying both sides by $x$, we get,
$⇒2x^2+1=\frac{17x}{6}$
$⇒2x^2-\frac{17x}{6}+1=0$
Multiplying both sides by 6, we get,
$\Rightarrow 12x^2-17x +6=0$
$\Rightarrow (3x-2)(4x-3)=0$
$\Rightarrow (3x-2)$ or $(4x-3)=0$
$\Rightarrow x=\frac{2}{3}$ or $x=\frac{3}{4}$
After checking the options we get, $x=\frac{3}{4}$
Hence, the correct answer is $\frac{3}{4}$.
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