Question

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

Answer 1

SOLUTION :  

Let the number be  x and its reciprocal be 1/x

A.T.Q

x + 1/x = 17/4

(x × x + 1)/x = 17/4

[By taking LCM]

( x² + 1 ) / x = 17/4

4( x² + 1 ) = 17x

4x² + 4 = 17x

4x² - 17x + 4 = 0

4x² - 16x - x + 4 = 0

[By middle term splitting]

4x( x - 4 ) - ( x - 4 ) = 0

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

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

x = 4  or  4x = 1  

x = 4  or  x = 1/4

x = 4 or x = ¼

Hence, the  numbers are 4 & ¼ .

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Let the number be x.
A. T. Q,
$\: \: \: \: \: \: \: x + \frac{1}{ x } = \frac{17}{4} \\ = > \frac{ {x}^{2} + 1}{x} = \frac{17}{4} \\ = > {x}^{2} + 1 = \frac{17x}{4} \\ = > 4 {x}^{2} + 4 = 17x \\ = > 4 {x}^{2} - 17x + 4 = 0 \\ = > 4 {x}^{2} - 16x - x + 4 = 0 \\ = > 4x(x - 4) - 1(x - 4) = 0 \\ = > (x - 4)(4x - 1) = 0 \\ = > x = 4 \: \: or \: \: \frac{1}{4}.$


So,
The number is 4 or 1/4.
Both the answers are correct.
If it would have been said that the number is positive integer or any integer or natural/whole number then, 4 will be the answer.



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