KUIS MATEMATIKA Kode: 01-5-5

------ Jawaban Terlampir ------

Mapel : Matematika
Tingkat : Olimpiade
Bab : Teori Bilangan

Pembahasan :
Misal 1 + 1/(2 + 1/x) = x

1 + 1/(2 + 1/x) = x
1 + 1/[(2x + 1)/x] = x
1 + x/(2x + 1) = x
(2x + 1 + x)/(2x + 1) = x
(3x + 1)/(2x + 1) = x
3x + 1 = 2x² + x
2x² - 2x - 1 = 0

Rumus ABC
D = b² - 4ac
D = (-2)² - 4(2)(-1)
D = 4 + 8
D = 12

X1 = (2 + √12)/4
X1 = (2 + 2√3)/4
X1 = 1/2(1 + √3)

X2 = (2 - 2√3)/4
X2 = 1/2(1 - √3)

Jawaban : B