SOLUTION: In the equation {{{x=((1-y)/(1+y))}}}, I know empirically that x = y when either of them has the value {{{sqrt( 2 ) -1}}}, but I don't know how to prove it algebraically. ANY he

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: In the equation {{{x=((1-y)/(1+y))}}}, I know empirically that x = y when either of them has the value {{{sqrt( 2 ) -1}}}, but I don't know how to prove it algebraically. ANY he      Log On


   

Question 1068984: In the equation x=%28%281-y%29%2F%281%2By%29%29, I know empirically that x = y when either of them has the value sqrt%28+2+%29+-1, but I don't know how to prove it algebraically.
ANY help greatly appreciated!
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
To prove it algebraically, simply SUBSTITUTE y = sqrt%282%29-1 into the right side.

Then simplify and check.