SOLUTION: Find two positive real numbers that differ by 1 and the product of 1.

Question 39599: Find two positive real numbers that differ by 1 and the product of 1.
Answer by kev82(151) (Show Source): You can put this solution on YOUR website!
Hi,
Let the two numbers be a, and b. Let a be the larger one. Then
a-b=1 so a=1+b
also ab=1, but a=1+b so (1+b)b=1
b^2+b-1=0
This is a quadratic equation, which we can solve by completing the square.
(b+1/2)^2-5/4=0
(b+1/2)^2=5/4
(Note b has to be posotive from question)

a=b+1 so

Don't forget to go back and check the answer is right by working out ab.
Hope that helps,
Kev
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