Diketahui bahwa [tex] 3^{(y-x)} (x+y)=1[/tex] dan [tex] (x+y)^{(x-y)} =3[/tex], maka [tex] x^{3y} =[/tex]

jawab

misal 
x + y = a
x - y = b

3^(y-x). (x+y) = 1
3^(-b) .(a) = 1
a= 3^(b)

(x+y)^(x-y) = 3
a^b = 3

(3^(b))^b = 3^1
3^(b²) = 2^1
b² = 1
b = 1   atau b = - 1

a^b = 3
untuk b = 1 --> a = 3
x+ y  = a = 3
x - y = b = 1...(+)
2x = 4
x = 2 --> y = 1

nilai x ^(3y) = 2^(3y) = (2)^3 = 8

untuk b = -1
a^b = 3 --> a^(-1) = 3
a = 1/3

x + y = 1/3
x - y = - 1 ...(+)
2x = -2/3
x = - 1/3
y = 2/3

nilai x^(3y) = (-1/3)^(3(2/3)  = (-1/3)^(2) =  1/9