Решите уравнение: (x^2+2 х) (х^2+2 х+2) = 3

Пусть x^2 + 2x = t, тогда

t (t + 2) = 3

t^2 + 2t - 3 = 0

D = 4 + 12 = 16 = 4^2

t₁ = ( - 2 + 4) / 2 = 1;

t₂ = ( - 2 - 4) / 2 = - 3;

x^2 + 2x = 1

x^2 + 2x - 1 = 0

D = 4 + 4 = 8

x₁ = ( - 2 + 2√2) / 2 = - 1 + √2;

x ₂ = ( - 2 - 2√2) / 2 = - 1 - √2;

x^2 + 2x = - 3

x^2 + 2x + 3 = 0

D = 4 - 4*3 < 0

∅ нет реш

Ответ

- 1 - √2;

- 1 + √2