Question

Tolong dijawab :
1. 4^3/2×3^1/2×12^1/2
2. 4^n÷16^-2n×32^-2n
3. jika 2^2x+2^-2x=23,maka 2^x+2^-x adalah

Answer 1

1) 4^(3/2) . 3^(1/2). 12(1/2)
= 2^2(3/2). 3^(1/2).(2^2.3)^(1/2)
= 2^(3). 3^(1/2). 2^(1) . 3^(1/2)
= 2^(3+1). 3^(1/2+1/2)
= 2^4. 3^1 = 16(3)= 28
.
2). 2^(2n) : 2^(-8n) x 2^(-10n)
= 2^(2n+8n-10n)
= 2^0 = 1
.
3)
misal a= 2^x dan b= 2^-x
maka (2^x)^2 + (2^-x)^2 = 23 --> a^2 +b^2 = 23
dan  ab = 1
.
a^2+b^2 =(a+b)^2 - 2(ab)
23 = (a+b)^2 - 2(1)
(a+b)^2 = 25
a+b= 5 atau a+b = -5