What is $x^3 + x + 1$ for $x=\frac{\sqrt 5 - 1}{2}$ 
What is $x^3 + x + 1$ for $x=\frac{\sqrt 5 - 1}{2}$

Of course we can subtitute and expand it
${(\frac{\sqrt 5 -1}{2})}^3 + \frac{\sqrt 5 -1}{2} + 1$
Is there a better way to do it?

Since $x^2=\frac{3-\sqrt{5}}{2}=1-x$, $x^3=x-x^2=2x-1$, so $x^3+x+1=3x$.
