\(\left|x^{2018}+|x-1|\right|=x^{2018}+2404\)

\(\Leftrightarrow x^{2018}+\left|x-1\right|=x^{2018}+2404\)

\(\Leftrightarrow\left|x-1\right|=2404\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=2404\\x-1=-2404\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2405\\x=-2403\end{cases}}}\)

\(|x^{2018}+|x-1||=x^{2018}+2404\)

\(\Leftrightarrow\orbr{\begin{cases}x^{2018}+|x-1|=-x^{2018}-2404\\x^{2018}+|x-1|=x^{2018}+2404\end{cases}\Leftrightarrow\orbr{\begin{cases}|x-1|=-\left(2x^{2018}+2404\right)\left(l\right)\\|x-1|=2404\left(n\right)\end{cases}}}\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=-2404\\x-1=2404\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2403\\x=2405\end{cases}}}\)

V...

\(\left|x^{2018}+\left|x-1\right|\right|=x^{2018}+2404\)

Ta thấy: \(x^{2018}\ge0\);\(\left|x-1\right|\ge0\)\(\Rightarrow x^{2018}+\left|x-1\right|\ge0\)

\(\Rightarrow\left|x^{2018}+\left|x-1\right|\right|=x^{2018}+2404\)

   \(\Leftrightarrow x^{2018}+\left|x-1\right|=x^{2018}+2404\) 

                          \(\left|x-1\right|=2404\)

\(\Rightarrow\orbr{\begin{cases}x-1=2404\\x-1=-2404\end{cases}}\Rightarrow\orbr{\begin{cases}x=2405\\x=-2403\end{cases}}\)

             Vậy \(x\in\left\{2405;-2403\right\}\)

giúp mình nha

Lập bảng

4037-2x=1 với \(x\le2018\)

2x=4036

x=2018(t/m)

4037=1(loại)

2x-4037=1 với x\(\ge2019\)

2x=4038

x=2019(t/m)