(x-1)^4-5(x^2-1)^2+4(x+1)^4=0
ну можно в степени возвести
а можно сделать замену
(x-1)^4-5(x-1)^2(x+1)^2+4(x+1)^4=0
(x + 1)^2 = t
(x - 1)^2 = u
u^2 - 5ut + 4t^2 = 0
D = 25t^2 - 16t^2 = 9t^2
u12 = (5t +- 3t)/2 = 4t t
(u - t)*(u - 4t) = 0
1. u = t
(x + 1)^2 = (x - 1)^2
(x + 1)^2 - (x - 1)^2 = 0
(x + 1 + x -1)(x + 1 - x + 1) = 0
4x = 0
x = 0
2. (x - 1)^2 = 4(x + 1)^2
(2(x + 1))^2 - (x - 1)^2 = 0
(2x + 2 + x - 1)(2x + 2 - x + 1) = 0
(3x + 1)(x + 3) = 0
x = -1/3
x = -3
x= {-3, -1/3. 0}
(x-1)^4-5(x^2-1)^2+4(x+1)^4=0
ну можно в степени возвести
а можно сделать замену
(x-1)^4-5(x^2-1)^2+4(x+1)^4=0
(x-1)^4-5(x-1)^2(x+1)^2+4(x+1)^4=0
(x + 1)^2 = t
(x - 1)^2 = u
u^2 - 5ut + 4t^2 = 0
D = 25t^2 - 16t^2 = 9t^2
u12 = (5t +- 3t)/2 = 4t t
(u - t)*(u - 4t) = 0
1. u = t
(x + 1)^2 = (x - 1)^2
(x + 1)^2 - (x - 1)^2 = 0
(x + 1 + x -1)(x + 1 - x + 1) = 0
4x = 0
x = 0
2. (x - 1)^2 = 4(x + 1)^2
(2(x + 1))^2 - (x - 1)^2 = 0
(2x + 2 + x - 1)(2x + 2 - x + 1) = 0
(3x + 1)(x + 3) = 0
x = -1/3
x = -3
x= {-3, -1/3. 0}