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Question : A number is greater than 58 times its reciprocal by $\frac{3}{4}$. What is the number?

Option 1: –8

Option 2: 12

Option 3: –12

Option 4: 8


Team Careers360 10th Jan, 2024
Answer (1)
Team Careers360 21st Jan, 2024

Correct Answer: 8


Solution : Let the number be $x$.
According to the question,
$\frac{58}{x}+\frac{3}{4}=x$
$\Rightarrow 4x^2-3x-232=0$
$\Rightarrow 4x^2-32x+29x-232=0$
$\Rightarrow 4x(x-8)+29(x-8)=0$
$\Rightarrow (4x+29)(x-8) =0$
$\Rightarrow (4x+29)=0$ or $(x-8) =0$
$\therefore x=\frac{-29}{4},8$
Hence, the correct answer is 8.

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