1. Jika a+b = 1 dan a^2 + b^2 = 2 maka a^4 + b^4 = ? 2. 3. Jika 3^x+2 + 9^x+1 = 810 maka 3^-3 = ?

1) (a + b) = 1
(a + b)^2 = 1^2
a^2 + 2ab + b^2 = 1
a^2 + b^2 + 2ab = 1
2 + 2ab = 1
2ab = -1
ab = -1/2

a^2 + b^2 = 2
(a^2 + b^2)^2 = 2^2
a^4 + 2a^2.b^2 + b^4 = 4
a^4 + b^4 + 2 (ab)^2 = 4
a^4 + b^4 + 2 (-1/2)^2 = 4
a^4 + b^4 + 2 (1/4) = 4
a^4 + b^4 = 4 - 1/2 = 7/2 = 3 1/2 = 3,5

2) (1/(1 + p))^5 . (1/(1 - p))^-7 . ((p - 1)/((1 + p))^-6
= (1 + p)^-5 . (1 - p)^7 . (p - 1)^-6 . (1 + p)^6
= (1 + p)^(-5 + 6) . (-1(p - 1))^7 . (p - 1)^-6
= (1 + p)^1 . (-1)^7 . (p - 1)^7 . (p - 1)^-6
= (p + 1) . -1 . (p - 1)^(7 + (-6))
= -1 (p + 1) (p - 1)
= -1 (p^2 - 1)
= 1 - p^2

3) 3^(x + 2) + 9^(x + 1) = 810
3^x . 3^2 + 9^x . 9^1 = 810
9 . 3^x + 9 . (3^x)^2 = 810 ====> misal 3^x = p
9p + 9p^2 - 810 = 0 =========> bagi 9
p^2 + p - 90 = 0
(p - 9)(p + 10) = 0
p = 9 atau p = -10
3^x = 9 atau 3^x = -10
3^x = 3^2 atau 3^x = 3^...
x = 2 atau tidak ada x yang memenuhi
3^(x - 3) = 3^(2 - 3) = 3^-1 = 1/3