Question

Giai phương trình (x^3+x^2)+(x^2+x)=0

Answer 1

\(x^3+x^2+x^2+x=0\)

\(\Rightarrow x.\left(x^2+2x+1\right)=0\)

TH1: x=0

TH2: \(x^2+2x+1=0\)

\(x^2+2x=-1\)

\(x.\left(x+2\right)=-1\)

Mà \(Ư\left(-1\right)=\left\{-1;1\right\}\)

x<x+2 => x=-1; x+2=1

Ta đều có x=-1

Vậy \(x\in\left\{-1;0\right\}\)

Answer 2

(x^3+x^2)+(x^2+x)=0

<=>x².(x+1)+x.(x+1)=0

<=>x.(x+1)(x+1)=0

<=>x=0 hoặc x=-1

Answer 3

(x^3+x^2)+(x^3+x)=0

<=>x^3+x^2+x^2+x=0

<=>x.(x^2+x+x+1)=0

 Do đó x=0

 Hoặc x^2+x+x+1=0

=>x.(x+1)+(x+1)=0

=>(x+1)²=0=>x=-1

 Vậy x E {-1;0}