1) x^3 +9 = (3 +x)^3
x^3 +9 = 27 +27x + 9x^2 +x^3
9x^2 +27x + 18 = 0
x^2 +3x +2 = 0
По т. Виета х1 = -1 и х2 = -2
2) 6х -5 = 4х =13
2х = 18
х = 9
3)4х^2 - 5 = 5x +1
4x^2 -5x -6 = 0
D = 121
x1 = 2, x2 = -3/4
4) Cosx + 9^x -2 = Cosx -3^(x+1) +16
9^x +3^(x+1) -18 = 0
3^2x +3^x*3 -18 = 0
3^x = t
t^2 +3t -18 = 0
по т. Виета t1 = -6, t2 = 3
a) 3^x = -6 б) 3^x = 3
нет решений x = 1
5)3^(x+2) = 7^x
3^x*3^2 = 7^x | : 7^x
(3/7)^x * 9 = 1
(3/7)^x = 9^-1
xlg(3/7) = -lg9
x = -lg9/lg(3/7)
6)Sin2x + 7^(x+2) = Cosx + 7^(x+2)
Sin2x -Cosx = 0
2SinxCosx -Cosx = 0
Cosx(2sinx -1) = 0
a) Cos x = 0 или б) 2Sinx -1 = 0
x =π/2 + πk , k Є Z Sinx = 1/2
x = (-1)^n π/6 + πn, n Є Z