Book Maths Puzzle Algebra

I am supposed to find two positive real numbers that differ by 1 and have a product of 1.
This is how I did this:
x(x+1) = 1
0+1=1

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I am trying to get through some problems....one of which is:
y = x^2 - 6x + 2
I'll be asking for many more but I will do one at a time. :)
~Jolene OK, I am so not worthy of your math wisdom :) (thank you for helping).
There are still a few I am lost on....I hope you have the time. :)
I am supposed to solve the equation and check for extraneous solutions:
(w-3)^1/2=(4w+15)^1/2
and
(x^2-5x+2)^1/2=x

OR

5/(y-3)=1+[(y+7)/(2y-6)]

Jon, you are helping me so much, I really do appreciate it cuz I am so lost on this stuff. Tutoring like this is my last hope. :)