Решение
(2^(x^2))^2 - 5*2^(x^2)*2^(2x) + 4*(2^(2x))^2 = 0 делим на (2^(2x))^2
[2^(x^2)/(2^(2x))]^2 - 5*(2^(x^2)/(2^(2x)) + 4 = 0
2^(x^2)/(2^(2x)) =Z
z^2 -5z + 4 = 0
z1 = 1
z2 = 4
1) 2^(x^2 - 2x) = 1
2^(x^2 - 2x) = 2^0
x^2 - 2x = 0x*(x - 2) = 0
x1 = 0
x2 = 2
2) 2^(x^2 - 2x) = 4
2^(x^2 - 2x) = 2^2
x^2 - 2x = 2
x^2 - 2x - 2 = 0
D = 4 + 4*1*2 = 12
x3 = (2 - 2√3)/2
x3 = 1-√3
x4 = 1+√3
Ответ: x1 = 0; x2 = 2; x3 = 1-√3; x4 = 1+√3