1/
Đặt `x/2018=y/2019=z/2020=k`
`=>x=2018k;y=2019k;z=2020k`
Khi đó
`(x-z)^2=(2018k-2020k)^2=(-2k)^2=4k^2`
`4(x-y).(y-z)=4.(2018k-2019k).(2019k-2020k)=4.(-k).(-k)=4k^2`
Do đó
`(x-z)^2=4(x-y)(y-z)`
2/
`(2bz-3cy)/a=(3cx-az)/(2b)=(ay-2bx)/(3c)`
`=>(2abz-3acy)/(a^2)=(6bcx-2abz)/(4b^2)=(3acy-6bcx)/(9c^2)`
Áp dụng tính chất dãy tỉ số bằng nhau
`(2abz-3acy)/(a^2)=(6bcx-2abz)/(4b^2)=(3acy-6bcx)/(9c^2)=(2abz-3acy+6bcz-2abz+3acy-6bcx)/(a^2+4b^2+9c^2)=0`
`=>2abz-3acy=6bcx-2abz=0`
`=>2bz=3cy;3cx=az;`
`=>z/(3c)=y/(2b);x/a=z/(3c)`
`=>x/a=y/(2b)=z/(3c)`