khó hiểu vcl

đúng lun ko hiểu một chút nào
 

Ta có: \(\dfrac{x+1}{2018}+\dfrac{x+1}{2019}+\dfrac{x+1}{2020}+\dfrac{x+1}{2021}=0\)

\(\Leftrightarrow x+1=0\)

hay x=-1

Cho a,b,c khác 0 t/m:
1/a+1/b+1/c=1/2018 và a+b+c=2018
cmr" 1/a^2019+1/b^2019+1/c^2019=1/(a^2019+b^2019+c^2019)

Ta có :

$gt\Rightarrow x^2-xy-(5x-5y)-x+8=0\Rightarrow (x-y)(x-5)-(x-5)=-3\Rightarrow (5-x)(x-y-1)=3$

Đến đây là dạng của phương trình ước số bạn chỉ cần xét ước của $3$ là sẽ tìm được nghiệm nguyên của $PT$

\(x^{2020}=x\Leftrightarrow x^{2020}-x=0\Leftrightarrow x\left(x^{2019}-1\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x^{2019}-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x^{2019}=1\end{cases}}\)

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

\(1+2+2^2+2^3+....+2^{2019}+2^{2020}\)

\(A=\left(1+2+2^2\right)+\left(2^3+2^4+2^5\right)+....+\left(2^{2016}+2^{2017}+2^{2018}\right)+2^{2019}+2^{2020}\)

\(A=\left(1+2+2^2\right)+2^3\left(1+2+2^2\right)+.....+2^{2016}\left(1+2+2^2\right)+2^{2019}+2^{2020}\)

\(A=7+2^3.7+2^6.7+2^9.7+....+2^{2016}.7+2^{2019}+2^{2020}\)

\(\text{Ta có:}2^{2019}+2^{2020}=8^{673}+8^{673}.2\equiv1+1.2\left(\text{mod 7}\right)\equiv3\left(\text{mod 7}\right)\Rightarrow A\text{ chia 7 dư 3}\)

\(\frac{x-4}{2021}+\frac{x-3}{2020}=\frac{x-2}{2019}+\frac{x-1}{2018}\)

\(\Leftrightarrow\left(\frac{x-4}{2021}+1\right)+\left(\frac{x-3}{2020}+1\right)=\left(\frac{x-2}{2019}+1\right)+\left(\frac{x-1}{2018}+1\right)\)

\(\Leftrightarrow\frac{x+2017}{2021}+\frac{x+2017}{2020}=\frac{x+2017}{2019}+\frac{x+2017}{2018}\)

\(\Leftrightarrow\frac{x+2017}{2021}+\frac{x+2017}{2020}-\frac{x+2017}{2019}-\frac{x+2017}{2018}=0\)

\(\Leftrightarrow\left(x+2017\right)\left(\frac{1}{2021}+\frac{1}{2020}-\frac{1}{2019}-\frac{1}{2018}\right)=0\)

Mà \(\left(\frac{1}{2021}+\frac{1}{2020}-\frac{1}{2019}-\frac{1}{2018}\right)\ne0\)

\(\Leftrightarrow x+2017=0\)

\(\Leftrightarrow x=-2017\)

Vậy ..

=> (x-4/2021 +1) + (x-3/2020 +1) = (x-2/2019 +1)+ (x-1/2018 +1)

=> x+2017/2021 + x+2017/2020 = x+2017/2019 + x+2017/2018

=> x+2017/2018 + x+2017/2018 - x+2017/2020 - x+2017/2021 = 0

=> (x+2017).(1/2018+1/2019+1/2020+1/2021) = 0

=> x+2017 = 0 ( vì 1/2018+1/2019+1/2020+1/2021 > 0 )

=> x=-2017

Vậy x=-2017

k mk nha

a, \(\dfrac{2017.2021-4031}{2020+2017.2018}\)

= \(\dfrac{2017\left(2018+3\right)-4031}{2020+2017.2018}\)

= \(\dfrac{2017.2018+2017.3-4031}{2020+2017.2018}\)

= \(\dfrac{2017.2018+2020}{2020+2017.2018}\)

= 1
@Nguyen Thi Ngoc Linh

Sửa đề: \(\left(\frac12+\frac13+\cdots+\frac{1}{2021}\right)\cdot x=\frac{2020}{1}+\frac{2019}{2}+\cdots+\frac{1}{2020}\)

Ta có: \(\frac{2020}{1}+\frac{2019}{2}+\cdots+\frac{1}{2020}\)

\(=\left(1+\frac{2019}{2}\right)+\left(1+\frac{2018}{3}\right)+\cdots+\left(1+\frac{1}{2020}\right)+1\)

\(=\frac{2021}{2}+\frac{2021}{3}+\cdots+\frac{2021}{2021}=2021\left(\frac12+\frac13+\cdots+\frac{1}{2021}\right)\)

Ta có: \(\left(\frac12+\frac13+\cdots+\frac{1}{2021}\right)\cdot x=\frac{2020}{1}+\frac{2019}{2}+\cdots+\frac{1}{2020}\)

=>\(x\left(\frac12+\frac13+\cdots+\frac{1}{2021}\right)=2021\left(\frac12+\frac13+\cdots+\frac{1}{2021}\right)\)

=>x=2021