If $\Phi$ and $\varphi$ are the two distinct solutions to the equation x^2=x+1, then what is the value of ($\Phi$ - $\varphi$)^2?

The solutions are    1/2 + √5/2      and    1/2 - √5/2

So we have

[  (1/2 + √5/2) - (1/2 - √5/2) ]^2  =

[ √5/2 + √5/2 ]^2  =

[ 2√5 / 2 ]^2

[ √5 ] ^2  =

5

EDITED