Question

Rozwiązać równania
a)
b)
c)

Answer 1

a)
(√2)^2x + 2^(-x) = 5/2
2^x + 1/2^x = 5/2
2^x = y
y + 1/y = 5/2
2y + 2/y = 5 ⇔ 4 + 1 = 5
2y = 4  => y = 2
2/y = 1 => y = 2 
2^x = 2
x = 1
b)
2^(2x) - 4^(-x) = 3/2
4^x - 1/4^x = 3/2
4^x = y
y - 1/y = 3/2
2y - 2/y = 3 ⇔ 4 - 1 = 5
2y = 4  => y = 2
2/y = 1 => y = 2
4^x = 2
2^(2x) = 2
2x = 1
x = 1/2
c)
2^(-2x) - 4^x + 3/2 = 0
1/4^x - 4^x + 3/2 = 0
4^x = y
1/y - y + 3/2 = 0
y - 1/y = 1,5 ⇔ 2 - 1/2 = 1,5
y = 2
4^x = 2
x = 1/2