Question

Tìm x:

\(2013\left|x+2015\right|+\left(x+2015\right)^2=2014\left|x+2015\right|\)

Answer 1

\(2013\left|x+2015\right|+\left(x+2015\right)^2=2014\left|x+2015\right|\)

\(\Rightarrow2013\left|x+2015\right|+\left|x+2015\right|^2=2014\left|x+2015\right|\)

Đặt: \(\left|x+2015\right|=l\ge0\) khi đó phương trình trở thành:

\(2013l+l^2=2014l\)

\(\Rightarrow l^2=l\Leftrightarrow l^2=l=0\)

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

Với \(l=0\) ta có: \(\left|x+2015\right|=0\Leftrightarrow x=-2015\)

Với \(l=1\) ta có: \(\left|x+2015\right|=1\Leftrightarrow\left[{}\begin{matrix}x+2015=1\\x+2015=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2014\\x=-2016\end{matrix}\right.\)