Solve $x^2-x-1<0$

$\left(\frac{1-\sqrt{5}}{2},\frac{1+\sqrt{5}}{2}\right)$ $\left(1,\frac{1+\sqrt{5}}{2}\right)$ $\left(0,\frac{1+\sqrt{5}}{2}\right)$ $\left(\frac{1-\sqrt{5}}{2},0\right)$

$\left(\frac{1-\sqrt{5}}{2},\frac{1+\sqrt{5}}{2}\right)$

Let us first factorize $x^2-x-1$ For that let $x^2-x-1=0$ $⇒x=\frac{1±\sqrt{1+4}}{2}=\frac{1±\sqrt{5}}{2}$ Now on the number line (x-axis), mark $x=\frac{1±\sqrt{5}}{2}$ From the sign scheme of $x^2-x-1$, which is shown in the figure, we have $x^2-x-1<0$ $⇒x∈\left(\frac{1-\sqrt{5}}{2},\frac{1+\sqrt{5}}{2}\right)$