Question : If the sum of a non-zero number and thrice its reciprocal is $\frac{52}{7}$. Find the number.
Option 1: 8
Option 2: 9
Option 3: 7
Option 4: 6
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Correct Answer: 7
Solution : Given: The sum of a non-zero number and thrice its reciprocal is $\frac{52}{7}$. Let the number be $x$. According to the question, $x+\frac{3}{x}=\frac{52}{7}$ $\Rightarrow 7x^2-52x+21=0$ $\Rightarrow (7x-3)(x-7)=0$ $\Rightarrow (7x-3)$ or $(x-7)=0$ $\Rightarrow x=7$ or $ \frac{3}{7}$ After checking the options, we get, $x=7$ Hence, the correct answer is 7.
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