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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