If the sum of two number is 5 and their product equals to 2 how

to find the sum of their inverses.(in simplified form)

Thanks for your help.

let the numbers be x & y
x + y = 5
xy = 2
1/x + 1/y
= (x + y)/(xy)
= 5/2

Regards.

Given sum, s, & product, p, of 2 numbers, they are the 2 solutions of the quadratic
x² - sx + p = 0

A quadratic whose roots are the reciprocals, y = 1/x, of those of a given quadratic, is obtained by reversing the order of coefficients:
py² - sy + 1 = 0

and the sum of its roots is
s/p = 5/2

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... confirming iceman's answer (which is even more direct).

And no, you don't have to find the individual numbers. But if you want to, use
(x+y)² - 4xy = (x-y)²

to obtain
x - y = ±√17

and thus
x,y = ½(5 ± √17) ≈ 0.438447187191169, 4.561552812808831

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And you can confirm iceman's answer by adding the reciprocals of these:

2/(5-√17) + 2/(5+√17) = 2(5 + √17 + 5 - √17)/(25 - 17) = 20/8
= 5/2

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Wow this comment box is great, I am so glad that I found this Math. section in yahoo. In few hours I learned more stuff than I would in few days alone. Thanks Fred you are great I wish I had you as my teacher. I also thank Ron, s22k and Iggy, you guys are all amazingly smart and kind.

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Hi Mike!

Let x be one number
5-x is the other number

x(5-x)=2
x² - 5x + 2 = 0
x²-5x+25/4=25/4-8/4
(x-5/2)² = 17/4

x =5/2 ± √(17/4)
5-x = 5/2 ∓ √(17/4)

So, you could either have, as valid pairs of numbers: