1) 2^x + 1 = 2^(x+2) - 2
2^x + 1 = 2^x*4 - 2
2^x*3 = 3
2^x = 1
x = 0
2) 4*2^(-2/(x+1)) - 8* 2^(-1/(x+1))*5^(-1/(x+1)) - 5*5^(-2/(x+1)) = 0
Делим всё на
5^(-2/(x+1))
4*(2/5)^(-2/(x+1)) - 8*(2/5)^(-1/(x+1)) - 5 = 0
Замена
(2/5)^(-1/(x+1)) = y > 0 при любом х
4y^2 - 8y - 5 = 0
D/4 = 4^2 - 4(-5) = 16 + 20 = 36 = 6^2
y1 = (4 - 6)/4 = -2/4 < 0 - не подходит<br>y2 = (4 + 6)/4 = 10/4 = 5/2
(2/5)^(-1/(x+1)) = 5/2
(5/2)^(1/(x+1)) = 5/2
1/(x+1) = 1
x = 0