Question

Tìm x biết : \(\left|x^4+x^2+1\right|=x^2-x+1\)

Answer 1

Vì `x^4>=0,x^2>=0`

`=>x^4+x^2+1>=1>0`

`=>|x^4+x^2+1|=x^4+x^2+1`

`=>x^4+x^2+1=x^2-x+1`

`=>x^2=-x`

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

`=>[(x=0),(x+1=0):}`

`=>[(x=0),(x=-1):}`

Vậy `x=0` hoặc `x=-1`

Answer 2

Ta có: \(\left|x^4+x^2+1\right|=x^2-x+1\)

\(\Leftrightarrow x^4+x^2+1-x^2+x-1=0\)

\(\Leftrightarrow x^4+x=0\)

\(\Leftrightarrow x\left(x+1\right)\left(x^2-x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)