I'm supposed to prove that all the solutions to X^2 = X + 1 are irrational.
I'm not sure exactly where to begin. I know by contradiction I would make it rational and replace x with A/B. Then work the problem through. After I worked it through I ended up with
0 = b/a + (b^2)/(a^2) and I'm not even sure if i'm on the right track even.
Do you any of you know?
Thanks for the help.