Question : The sum of a non-zero number and twice its reciprocal is $\frac{33}{4}$. Find the number.
Option 1: 9
Option 2: 10
Option 3: 11
Option 4: 8
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Correct Answer: 8
Solution :
Let the non-zero integer be $x$.
Given: The sum of a non-zero number and twice its reciprocal is $\frac{33}{4}$.
$\Rightarrow x+\frac{2}{x}=\frac{33}{4}$
$\Rightarrow 4x^2-33x+8=0$
$\Rightarrow 4x^2-32x-x+8=0$
$\Rightarrow 4x(x-8)-(x-8)=0$
$\Rightarrow (4x-1)(x-8)=0$
$\Rightarrow (4x-1)=0 \;or\;(x-8)=0$
$\therefore x=8, \frac{1}{4}$
Hence, the correct answer is 8.
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