Persamaan kuadrat dengan koenfisien bulat akar akarnya cos 72 dan cos 144 adalah? A. x^2 + 2x - 4 B. x^2 - 4x + 2 C. 2x^2 + 4x - 1 D. 4x^2 + 2x - 1

x1 + x2 = cos 144 + cos 72
= 2 cos (144 + 72)/2 cos (144 - 72)/2
= 2 cos 108° cos 36°
= 2 . - cos 72° cos 36°
= -2 sin 18° cos 36°
= -2 (√5 - 1)/4 . (√5 + 1)/4
= -2 (5 - 1)/16
= -2 (4)/16
= -8/16
= -1/2

x1.x2 = cos 144° cos 72°
= 1/2 (cos (144° + 72°) + cos (144° - 72°))
= 1/2 (cos 216° + cos 72°)
= 1/2 (- cos 36° + sin 18°)
= 1/2 (sin 18° - cos 36°)
= 1/2 ((√5 - 1)/4 - (√5 + 1)/4)
= 1/2 (-2/4)
= -2/8
= -1/4
Persamaan kuadrat
x^2 - (x1 + x2)x + x1.x2 = 0
x^2 - (-1/2) x + (-1/4) = 0 ====> kali 4
4x^2 + 2x - 1 = 0