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

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

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

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 \(x\in\left\{2405;-2403\right\}\)

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

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

\(\Rightarrow\left|x+1\right|=2404\)

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

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)

\(\frac{x-2017}{2018}-\frac{x-2018}{2017}=\frac{2017}{x-2018}-\frac{2018}{x-2017}\)

\(\Leftrightarrow\)\(\frac{2017\left(x-2017\right)-2018\left(x-2018\right)}{2017.2018}=\frac{2017\left(x-2017\right)-2018\left(x-2018\right)}{\left(x-2017\right)\left(x-2018\right)}\)

Do \(2017\left(x-2017\right)-2018\left(x-2018\right)\ne0\) nên \(\left(x-2017\right)\left(x-2018\right)=2017.2018\)

\(\Leftrightarrow\)\(x^2-4035x+2017.2018=2017.2018\)

\(\Leftrightarrow\)\(x\left(x-4035\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\left(l\right)\\x=4035\left(n\right)\end{cases}}\)

Vậy x = 4035 

a, Vì -2018 khác 0

=> x-11=0

=> x=11

b, Vì -2018 < 0

=> x+13 > 0

=> x > -13

c, Vì 2018 > 0 => 2x-10 > 0

=> 2x > 10

=> x > 5

d, => x-3=0 hoặc 3x-9=0

=> x=3

e, Vì x-1 < x+5 

=> x-1 < 0 và x+5 > 0

=> x < 1 và x > -5

=> -5 < x < 1

Tk mk nha