Log5(x^6+9x^4+27x^2+27)=3
x^6 + 9x^4 + 27x^2 + 27 = 5^3
x^6 + 9x^4 + 27x^2 + 27 = 125
Замена переменных
t = x^2
t^3 + 9t^2 + 27t + 27 = 125
(t^3 + 3*3*t^2 + 3*3^2*t + 3^3)) - 125 = 0
(t + 3)^3 - 5^3 = 0
(t - 2)(t^2 + 11t + 49)=0
t - 2 = 0 t^2 + 11t + 49 = 0
t = 2 D = 11^2 - 4*49 = 121 - 196 = -75
Находим значения х
x^2 = 2
x1 = корень(2)
x2 = -корень(2)