Question

Уравнение (x2 + 2x + 2) ∙ (x2 + 2x – 9) + 10 = 0 приведи к квадратному.
Найди решение данного уравнения.
y2 – ∙ y –= 0
x1 = ; x2 = ; x3 = .

Answer 1

$\displaystyle (x^2+2x+2)(x^2+2x-9)=10=0\\x^4+2x^3-9x^2+2x^3+4x^2-18x+2x^2+4x-18+10=0\\x^4+4x^3-3x^2-14x-8=0\\x^4+x^3+3x^2-6x^2-6x-8x-8=0\\x^3(x+1)+3x^2(x+1)-6x(x+1)-8(x+1)=0\\(x+1)(x^3+3x^2-6x-8)=0\\(x+1)((x-2)(x^2+2x+4)+3x(x-2))=0\\(x+1)(x-2)(x^2+2x+4+3x)=0\\(x+1)(x-2)(x^2+5x+4)=0\\(x+1)(x-2)(x^2+4x+x+4)=0\\(x+1)(x-2)(x(x+4)+x+4)=0\\(x+1)(x-2)(x+4)(x+1)=0\\(x+1)^2(x-2)(x+4)=0\\(x+1)^2=0,x-2=0,x+4=0\\x_1=-4,x_2=-1,x_3=2$