Question

GPT: |x+1|+|x^2+4x+3|=x^3+1

Answer 1

\(\left|x+1\right|+\left|x^2+4x+3\right|=x^3+1\)

\(\Leftrightarrow\left|x+1\right|+\left|x^2+4x+3\right|-x^3-1=0\)

\(\Leftrightarrow\left|x+1\right|+\left|\left(x+1\right)\left(x+3\right)\right|-x^3-1=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\x+3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-3\end{cases}}\)

Vậy nghiệm phương trình là: {-1; -3}