Giải phương trình : | x^2 +x+1| +x|x-2|=x+3

$|x^2+x+1|+x|x-2|=x+3$

⇔ \(\left[ \begin{array}{l}x^2+x+1+x(x-2)=x+3\\x^2+x+1+x(2-x)=x+3\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}x^2+x+1+x^2-2x-x-3=0\\x^2+x+1+2x-x^2-x-3=0\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}2x^2-2x-2=0\\2x-2=0\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}2(x^2-x-1)=0\\2(x-1)=0\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}x^2-x-1=0\\x-1=0\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}x=\frac{1+\sqrt{5}}{2} hoặc…x=\frac{1-\sqrt{5}}{2} \\x=1\end{array} \right.\)