Question : A positive number is greater than thrice its reciprocal by $\frac{26}{3}$. What is the number?
Option 1: $10$
Option 2: $11$
Option 3: $9$
Option 4: $8$
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Correct Answer: $9$
Solution : Let the number be $x$. According to the question, $x\text{ – $\frac{3}{x}$ = $\frac{26}{3}$}$ or, $3x^{2} – 9= 26x$ or, $3x^{2} –26x – 9 = 0$ or, $3x^{2} + 1x –27x – 9 = 0$ or, $x(3x+1)– 9(3x+1)=0$ or, $(3x+1)(x–9)=0$ or, $x = 9, -\frac{1}{3}$ As per the given condition, the number can't be negative. So, the number is $9$. Hence, the correct answer is $9$.
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