Question

Prove that the roots of the equation \(x^3 - 24x^2 + 80x - 64 = 0\) are \(\sec^2\frac{\pi}{7}, \sec^2 \frac{2\pi}{7}, \sec^2 \frac{3\pi }{7}\)

Answer 1

So I guess we first have to construct an equation with roots \(\cos \frac{2\pi}7, \cos \frac{4\pi}7, \cos \frac{6\pi}7\)

Answer 2

Never mind, got it.