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\(\dfrac{y+z+t-2020x}{x}=\dfrac{z+t+x-2020y}{y}=\dfrac{t+x+y-2020z}{z}=\dfrac{x+y+z-2020t}{t}=\dfrac{-2017\left(x+y+z+t\right)}{x+y+z+t}=-2017\\ \Leftrightarrow\left\{{}\begin{matrix}y+z+t-2020x=-2017x\\z+t+x-2020y=-2017y\\t+x+y-2020z=-2017z\\x+y+z-2020t=-2017t\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+y+z+t=2x\\x+y+z+t=2y\\x+y+z+t=2z\\x+y+z+t=2t\end{matrix}\right.\\ \Leftrightarrow x=y=z=t=\dfrac{x+y+z+t}{2}=1010\\ \Leftrightarrow A=1010\left(2019-2020+2021-2022\right)=1010\left(-2\right)=-2020\)
\(\frac{x}{y+z+t}=\frac{y}{x+z+t}=\frac{z}{x+y+t}=\frac{t}{x+y+z}=\frac{x+y+z+t}{3\left(x+y+z+t\right)}=\frac{1}{3}\)
\(3x=y+z+t\)
\(3y=x+z+t\)
\(3x+3y=x+y+2z+2t\)
\(x+y=z+t\)
Tương tự ta được
\(y+z=x+t\)
P=1+1+1+1=4
TA CÓ : ( x / y + z + t ) + 1 = ( y / z +t + x ) + 1 = ( t / x + y + z ) + 1
Suy ra : x+y+z+t / y+z+t = x+y+z+t / z+t+x = x+y+z+t / t+x+y = x+y+z+t / x+y+z
do x+y+z+t khác 0 suy ra x=y=z=t suy ra M= 1+1+1+1 =4 
tích đúng nha
Vô đây: http://olm.vn/hoi-dap/question/300416.html
Bài đung 100%
Lần sau em nên ghi đúng đề:
\(\frac{y+z+t-nx}{x}=\frac{z+t+x-ny}{y}=\frac{t+x+y-nz}{z}=\frac{x+y+z-nt}{t}\)
=> \(\frac{y+z+t}{x}-n=\frac{z+t+x}{y}-n=\frac{t+x+y}{z}-n=\frac{x+y+z}{t}-n\)
=> \(\frac{y+z+t}{x}=\frac{z+t+x}{y}=\frac{t+x+y}{z}=\frac{x+y+z}{t}=\frac{3x+3y+3z+3t}{x+y+z+t}=3\)
Mà x + y + z + t = 2020
=> \(\frac{2020-x}{x}=\frac{2020-y}{y}=\frac{2020-z}{z}=\frac{2020-t}{t}=3\)
=> \(\frac{2020}{x}-1=\frac{2020}{y}-1=\frac{2020}{z}-1=\frac{2020}{t}-1=3\)
=> \(\frac{2020}{x}-1+1=\frac{2020}{y}-1+1=\frac{2020}{z}-1+1=\frac{2020}{t}-1+1=3+1\)
=> \(\frac{2020}{x}=\frac{2020}{y}=\frac{2020}{z}=\frac{2020}{t}=4\)
=> \(x=y=z=t=505\)
=> \(P=x+2y-3z+t=505+2.505-3.505+505=505\)