Question

The sum of numbers and it's reciprocal is 17 /4 find the numbers

Answer 1

Hi ,

Let the number = x

Reciprocal of the number = 1/x

x + 1/x = 17/4

( x² + 1 ) / x = 17/4

4( x² + 1 ) = 17x

4x² - 17x + 4 = 0

4x² - 16x - x + 4 = 0

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

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

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

x = 4 or x = 1/4

Therefore ,

Required numbers are ,

x = 4 , 1/x = 1/4

Or

x = 1/4 or 1/x = 4

I hope this helps you.

:)