Question

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Cho 3 số x,y,z,t thỏa mãn

\(\frac{y+z+t-mc}{x}=\frac{z+t+x-ny}{y}=\frac{t+x+y-nz}{z}=\frac{x+y+z-nt}{t}\)

và x+y+z+t=2020

TÍnh P=x+2y-3z+t

Answer 1

[Nguyễn Linh Chi]

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

=> \(\frac{2020-x}{x}=\frac{2020-y}{y}=\frac{2020-z}{z}=\frac{2020-t}{t}=3\)

=> \(\frac{2020}{x}-1=\frac{2020}{y}-1=\frac{2020}{z}-1=\frac{2020}{t}-1=3\)

=> \(\frac{2020}{x}-1+1=\frac{2020}{y}-1+1=\frac{2020}{z}-1+1=\frac{2020}{t}-1+1=3+1\)

=> \(\frac{2020}{x}=\frac{2020}{y}=\frac{2020}{z}=\frac{2020}{t}=4\)

=> \(x=y=z=t=505\)

=> \(P=x+2y-3z+t=505+2.505-3.505+505=505\)