[tex]x^2-x-1=0 \\
\Delta=(-1)^2-4.1.(-1)=1+4=5 \\
\boxed{\phi=\frac{1+\sqrt5}{2}} \\
\\
\phi ^2 =\left (\frac{1+\sqrt{5}}{2} \right )^2=\frac{(1+\sqrt{5})^2}{4}=\frac{1+2\sqrt{5}+5}{4}= \\
\\
\frac{6+2\sqrt5}{4}=\frac{3+\sqrt5}{2}=\frac{2+1+\sqrt5}{2}=\frac{2}{2}+\frac{1+\sqrt5}{2}=\boxed{\phi+1}[/tex]