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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