Question

Решите уравнения:
(x^2-4x)^2+9(x^2-4x)+20=0;
(x^2+x)(x^2-x-5)=84

Answer 1

1) (x^2 - 4x)^2 + 9(x^2-  4x) + 20 = 0
x^4 - 8x^3 + 16x^2 + 9x^2 - 36x + 20 = 0
x^4 - 2x^3 - 6x^3 + 25x^2 - 26x - 10x + 20 = 0
x^4 - 2x^3 - 6x^3 + 12x^2 + 13x^2 - 26x - 10x + 20 = 0
x^3 * (x - 2) - 6x^2 * (x - 2) + 13x(x - 2) - 10(x - 2) = 0
(x - 2)(x^3 - 6x^2 + 13x - 10) = 0
(x - 2)(x^3 - 2x^2 - 4x^2 + 8x + 5x - 10) = 0
(x - 2)(x^2 * (x - 2) - 4x(x - 2) + 5(x - 2)) = 0
(x - 2)(x - 2)(x^2 - 4x + 5) = 0
(x - 2)^2 * (x^2 - 4x + 5) = 0

(x - 2)^2 = 0
x^2 - 4x + 5 = 0

x = 2
x ∉ R

Ответ: x = 2

2) Второе не решается. Только графиком...