\(x\left(x-2022\right)-2x+4044=0\\ \Rightarrow x\left(x-2022\right)-2\left(x-2022\right)=0\\ \Rightarrow\left(x-2022\right)\left(x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=2022\\x=2\end{matrix}\right.\)

x(x-2022)-2x+4044=0

\(x^2-2022x-2x+4044=0\)

\(x^2-2x-2022x+4044=0\)

\(\left(x^2-2x\right)-\left(2022x-4044\right)=0\)

\(x\left(x-2\right)-2022\left(x-2\right)=0\)

\(\left(x-2\right)\left(x-2022\right)=0\)

\(x-2=0\)

\(x-2022=0\)

<=> \(x=\left\{2;2022\right\}\)

gọi 2021-x = a

2023-x=b

2x-4044=c

ta có a + b + c=2021-x+2023-x+2x-4044=0

suy ra a + b = -c

suy ra (a+b)^3 =-c^3

ta có a^3 + b^3 + c^3=(a+b)^3 -3ab(a+b) + c^3 = -c^3 +3abc +c^3 = 3abc 

ta có (2021-x)^3 + (2023-x)^3 + (2x-4044)^3 = 0

=> 3(2021-x)(2023-x)(2x-4044)=0

=> th 1 x = 2021,  th 2 x = 2023; th3 x = 2022

\(\dfrac{x}{y+z-3}=\dfrac{y}{x+z}=\dfrac{z}{x+y+3}=\dfrac{x+y+z}{2\left(x+y+z\right)}=\dfrac{1}{2}=\dfrac{1}{4044\left(x+y+z\right)}\)

\(\Rightarrow\left\{{}\begin{matrix}y+z-3=2x\\x+z=2y\\x+y+3=2z\end{matrix}\right.\) và \(4044\left(x+y+z\right)=2\)

\(\Rightarrow\left\{{}\begin{matrix}x+y+z=3x+3\\x+y+z=3y\\x+y+z=3z-3\end{matrix}\right.\\ \Rightarrow3x+3=3y=3z-3\\ \Rightarrow x+1=y=z-1\)

\(\left\{{}\begin{matrix}x=y-1\\z=y+1\end{matrix}\right.\)

Lại có \(4044\left(x+y+z\right)=2\)

\(\Rightarrow4044\left(y-1+y+y+1\right)=2\\ \Rightarrow4044\cdot3y=2\\ \Rightarrow y=\dfrac{1}{674}\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{673}{674}\\z=\dfrac{675}{674}\end{matrix}\right.\)

Đáp án:

`649/36` 

Giải thích các bước giải:

 `27`  x  `171717/272727`  `+`  `373737/363636`  `=`

 Rút gọn Phân số ta được:

`=`  `27`  x `17/27`  `+`  `37/36` 

`=`   `17`  `+`  `37/36`  `=`  `649/36` 

Hai số lẻ liên tiếp là:

2021 và 2023

Số bé là:2021

Hok tốt nha

Số bé nhất là 2021

Hok tốt 

Kb với mình nhé 

c 212121/353535

=212121:21/353535:35

=10101/10101

=212121:10101/353535:10101

=21/35