=36^ is a root of which of the following equations?

Question

$\alpha=\sin36^\circ$ is a root of which of the following equations?

Accepted Answer

$$\sin36^\circ = \frac{\sqrt{10-2\sqrt5}}4 \implies x^2 = \frac{10-2\sqrt5}{16} \implies 16x^2 = 10-2\sqrt5 \implies 16x^2-10=-2\sqrt5$$

Squaring: $256x^4-320x^2+100 = 20 \implies 256x^4-320x^2+80=0$. Dividing by 16:

$16x^4-20x^2+5=0$

Solutions · 1