Question

the sum of a no.and it's reciprocal is 17/4.find the number

Answer 1

Well, the reciprocal of an integer is 1 divided by that integer. So, the equation you get is:

x + 1/x = 17/4

x can be re-written as x^2/x, so you have (x^2 + 1)/x =17/4

Using cross multiplication, you end up with 4x^2 + 4 =17x, and if you subtract each side by 17x, you end up with

4x^2 - 17x + 4 = 0

What you do next is factor this equation, so you mulitply the "a" value and the "c" value. Since "a" is 4 and "c" is 4, you get 16. Now you need to find the factors of 16 that add up to the "b" value, or -17.

You end up with (4x-1) and (x-4), so your factors are 4 and 1/4.

So, the answer to the problem is that the integer is 4 and its reciprocal is 1/4

Answer 2

Let the no. be X
then.,
X + 1/X = 17/4
X^2 + 1 = 17/4 X
4X^2 + 4 = 17 X
4X^2 -17 X + 4 =0
4X^2 - 16X - X + 4 =0
4X ( X-4 ) -1 ( X-4 ) =0
( 4X-1 ) ( X-4 ) =0
X= 1/4. &. X = 4

HOPE IT HELPS
PLSS MARK BRAINLIEST