Problem - 4752
Solve $x^4-x^2-1=0$.
Let $y=x^2$, then applying the quadratic formula leads to $y=\frac{1\pm\sqrt{5}}{2}$. Because it is clear that $y=x^2\ge 0$, therefore $$y=\frac{1+\sqrt{5}}{2}\implies x = \boxed{\sqrt{\frac{1+\sqrt{5}}{2}}}$$
Solve $x^4-x^2-1=0$.
Let $y=x^2$, then applying the quadratic formula leads to $y=\frac{1\pm\sqrt{5}}{2}$. Because it is clear that $y=x^2\ge 0$, therefore $$y=\frac{1+\sqrt{5}}{2}\implies x = \boxed{\sqrt{\frac{1+\sqrt{5}}{2}}}$$