KUIS MATEMATIKA Kode: 04-3-6

Mapel : Matematika
Kelas : X SMA
Bab : Persamaan Kuadrat

Pembahasan :
Anggap n = x

9ⁿ + 9¯ⁿ - 3^(2 + n) + 3²¯ⁿ + 16 = 0
3²ⁿ + 3¯²ⁿ - 3ⁿ . 9 + 1/3ⁿ . 9 + 16 = 0
3²ⁿ + 3¯²ⁿ = 3ⁿ . 9 - 1/3ⁿ . 9 - 16

Maka...
(3ⁿ - 3¯ⁿ)² = 3²ⁿ - 1 - 1 + 3¯²ⁿ
(3ⁿ - 3¯ⁿ)² = 3²ⁿ + 3¯²ⁿ - 2
(3ⁿ - 3¯ⁿ)² = (3ⁿ . 9 - 1/3ⁿ . 9 - 16) - 2
(3ⁿ - 3¯ⁿ)² = (3ⁿ . 9 - 1/3ⁿ . 9 - 18)
(3ⁿ - 3¯ⁿ)² = 9(3ⁿ - 1/3ⁿ) - 18
(3ⁿ - 3¯ⁿ)² = 9(3ⁿ - 3¯ⁿ) - 18

Misal (3ⁿ - 3¯ⁿ) = a
a² = 9a - 18
a² - 9a + 18= 0
(a - 6)(a - 3) = 0
a = 6
(3ⁿ - 3¯ⁿ) = 6

a = 3
(3ⁿ - 3¯ⁿ) = 3

Jawaban : D