Question

[Đỗ Tấn Hoàng]

cho ba số x,y,z thỏa mãn \(\frac{x}{2017}=\frac{y}{2018}=\frac{z}{2019}\)

Chứng minh :  4.(x-y)(y-z)=\(\left(z-x\right)^2\)

giúp mình vs

Answer 1

[Kaori Miyazono]

xin loi , may tinh minh hong unikey

Dat \(\frac{x}{2017}=\frac{y}{2018}=\frac{z}{2019}=k\)

Suy ra \(x=2017k;y=2018k;z=2019k\)

Khi đó 4.(x-y).(y-z) = \(4.\left(2017k-2018k\right).\left(2018k-2019k\right)=4.\left(-k\right).\left(-k\right)=4k^2\)

\(\left(z-x\right)^2=\left(2019k-2017k\right)^2=\left(2k\right)^2=4k^2\)

Nen \(4.\left(x-y\right).\left(y-z\right)=\left(z-x\right)^2\)