Dễ thấy \(VT\ge0\Rightarrow2020x\ge0\Leftrightarrow x\ge0\)

\(\Rightarrow pt\Leftrightarrow2019x+\frac{2019.2020}{2}=2020x\)

\(\Leftrightarrow x=2019.1010\)

            Bài làm :

Ta có :

\(x+2x+3x+...+2020x=2020.2021\)

\(\Leftrightarrow x\left(1+2+3+...+2020\right)=2020.2021\)

\(\Leftrightarrow x.\frac{\left(2020+1\right).2020}{2}=2021.2020\)

\(\Leftrightarrow x.\frac{2021.2020}{2}=2021.2020\)

\(\Leftrightarrow x=2\)

Vậy x=2

\(x+2x+3x+...+2020x=2020\cdot2021\) 

\(x\left(1+2+3+...+2020\right)=2020\cdot2021\) 

1 + 2 + 3 ... + 2020 

Số số hạng : 

\(\left(2020-1\right):1+1=2020\) 

Tổng : 

\(\left(2020+1\right)\cdot2020:2=2021\cdot1010\) 

\(2021\cdot1010\cdot x=2020\cdot2021\) 

\(1010x=2020\) 

\(x=2\)

Ta có : \(\left(2020.x^2+2021\right).\left(x^2-1\right).\left(2.x+1\right)=0\)

\(\Leftrightarrow\hept{\begin{cases}2020.x^2+2021=0\\x^2-1=0\\2.x+=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x\notinℝ\\x=\pm1\\x=-\frac{1}{2}\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=1\\x=-1\\x=-\frac{1}{2}\end{cases}}\)

Vậy \(x=\left\{\pm1;-\frac{1}{2}\right\}\)

f(x) = \(\left(x^6-2019x^5\right)-\left(x^5-2019x^4\right)+\left(x^4-2019x^3\right)-\left(x^3-2019x^2\right)+\left(x^2-2019x\right)-\left(x-2019\right)+1\)

= \(x^5\left(x-2019\right)-x^4\left(x-2019\right)+x^3\left(x-2019\right)-x^2\left(x-2019\right)+x\left(x-2019\right)-\left(x-2019\right)+1\)

Thay x = 2019 vào f(x), ta có:

f(2019) = 0 + 0 + 0 + 0 + 0 +0 + 1 = 1

\(f\left(2019\right)=x^{100}-\left(2019+1\right)x^{99}+\left(2019+1\right)x^{98}-....+\left(2019+1\right)x^2-\left(2019+1\right)x+2000\)

\(=x^{100}-\left(x+1\right)x^{99}+\left(x+1\right)x^{98}-...+\left(x+1\right)x^2-\left(x+1\right)x+2000\)

\(=x^{100}-x^{100}-x^{99}+x^{99}+x^{98}-...+x^3+x^2-x^2-x+2000\)

\(=-x+2000=-2019+2000\)

\(=-19\)

\(D=4x^2-2x+3x\left(x-5\right)=4x^2-2x+3x^2-15x=7x^2-17x=7\left(-1\right)^2-17\left(-1\right)=24\)

\(E=x^{10}-2020x^9+2020x^8-2020x^7+...+2020x^2-2020x=x^9\left(x-2019\right)-x^8\left(x-2019\right)+x^7\left(x-2019\right)-...-x^2\left(x-2019\right)+x\left(x-2019\right)-x=x^9\left(2019-2019\right)-...+x\left(2019-2019\right)-2019=-2019\)

2021 - x + 2021(x - 2020x) = 0

<=> 2021 - x + 2021 - 4082420 = 0

<=> -x - 4082420 = 0

<=> x = -4082420