Question

Cho 3 số x, y, z thỏa mãn: \(\dfrac{x}{2018}=\dfrac{y}{2019}=\dfrac{z}{2020}\)

CMR: \(\left(x-z\right)^3=8\left(x-y\right)^2\left(y-z\right)\)

HELP ME!

Answer 1

Lời giải:

Đặt $\frac{x}{2018}=\frac{y}{2019}=\frac{z}{2020}=a$

$\Rightarrow x=2018a; y=2019a; z=2020a$

$\Rightarrow (x-z)^3=(2018a-2020a)^3=(-2a)^3=-8a^3(1)$

Mặt khác:

$8(x-y)^2(y-z)=8(2018a-2019a)^2(2019a-2020a)=8a^2.(-a)=-8a^3(2)$

Từ $(1); (2)$ ta có đpcm.