Question

(x²+3x) (x² + 3x − 2) = 8

Answer 1

(x/2+3x)(x/2+3x-2)=8

(x/2-3x)/2-3x)-8=0

t=x/2-3x

t/2-2t-8=0

t=2t=4

Answer 2

Ответ: x₁=-4,  x₂=1,  x₃=-1,  x₄=-2.

Объяснение:

$(x^2+3x)*(x^2+3x-2)=8.$

Пусть x²+3x=t.               ⇒

$t*(t-2)=8\\\\t^2-2t-8=0\\\\t^2-4t+2t-8=0\\\\t*(t-4)+2*(t-4)=0\\\\(t-4)*(t+2)=0\\\\t-4=0\\\\t_1=4.\\\\t+2=0\\\\t_2=-2.$

1. t₁=4.

$x^2+3x=4\\\\x^2+3x-4=0\\\\x^2+4x-x-4=0\\\\x*(x+4)-(x+4)=0\\\\(x+4)*(x-1)=0\\\\x+4=0\\\\x_1=-4.\\\\x-1=0\\\\x_2=1.$

2. t₂=-2.

$x^2+3x=-2\\\\x^2+3x+2=0\\\\x^2+x+2x+2=0\\\\x*(x+1)+2*(x+1)=0\\\\(x+1)*(x+2)=0\\\\x+1=0\\\\x_3=-1.\\\\x+2=0\\\\x_4=-2.$