Nilai (x + y) yang merupakan solusi dari sistem persamaan eksponensial : [tex]4^{x+1} + 2^{y} = 20 2^{x-1} - 2^{y} = -3 [/tex] adalah ..........................

2^x = a
2^y = b

4^(x + 1) + 2^y = 20
2^(2x + 2) + 2^y = 20
4a² + b = 20 ... (1)

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

Substitusi kan pers (2) ke pers (1)
4a² + 1/2 a + 3 = 20
8a² + a - 34 = 0
(8a + 17)(a - 2) = 0
a = -17/8 tdk memenuhi
a = 2
2^x = 2 --> x = 1

a = 2
b = 1/2 a + 3 = 4
b = 2^y
2^y = 4
y = 2

x + y = 1 + 2 = 3

Persamaan eksponen

4^(x+1) + 2^y = 20
2^(x-1)  - 2^y = - 3
jumlahkan

4^(x+1) + 2^(x-1) =  17
4^x . 4 + 2^x . 1/2 = 17
4 (2^x)^2 + 1/2 (2^x) = 17 ...kalikan 2
8 (2^x)^2 + (2^x) - 34 =0
2^x = a --> a> 0
8a^2 + a - 34 = 0
(a  -  2)(8a + 17) = 0
a= 2
2^x = 2 = 2^1
x = 1

2^(x-1) - 2^y = - 3
2^(1-1) - 2^y = - 3
2^0 - 2^y = - 3
1 - 2^y = - 3
2^y = 4 --> 2^y = 2^2
y = 2

x + y = 1 + 2= 3