The sum of a number and its reciprocal is $\frac{17}{4}$. Find the number.

Given:

The sum of a number and its reciprocal is $\frac{17}{4}$.

 To do:

We have to find the number.

Solution:

Let the number be $x$.

According to the question,

$x+\frac{1}{x}=\frac{17}{4}$

$\frac{x(x)+1}{x}=\frac{17}{4}$

$\frac{x^2+1}{x}=\frac{17}{4}$

$4(x^2+1)=17(x)$

$4x^2+4=17x$

$4x^2-17x+4=0$

Solving for $x$ by factorization method, we get,

$4x^2-16x-x+4=0$

$4x(x-4)-1(x-4)=0$

$(4x-1)(x-4)=0$

$4x-1=0$ or $x-4=0$

$4x=1$ or $x=4$

$x=\frac{1}{4}$ or $x=4$

The required number is $4$ or $\frac{1}{4}$. 

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Updated on: 10-Oct-2022

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