Question

Cho ba số x, y, z đôi một phân biệt thỏa mãn \(\dfrac{x}{2015}=\dfrac{y}{2016}=\dfrac{z}{2017}\)
Vậy \(\left(x-z\right)^3:\left[\left(x-y\right)^2\left(y-z\right)\right]=.......\)

Answer 1

Đặt \(\dfrac{x}{2015}=\dfrac{y}{2016}=\dfrac{z}{2017}=k\)

\(\Rightarrow x=2015k;y=2016k;z=2017k\) \(\left(1\right)\)

Thay (1) vào đề bài ta được:

\(\left(2015k-2017k\right)^3:\left[\left(2015k-2016k^2\right)\left(2016k-2017k\right)\right]\)

\(=\left(-2k\right)^3:\left[-k^2\left(-k\right)\right]\)

\(=-8k^3:\left(-k\right)^3\)

\(=8\)

Vậy \(\left(x-z\right)^3:\left[\left(x-y\right)^2\left(y-z\right)\right]=8.\)

Answer 2

nhất,nhị, tam.....bát

Answer 3

Đặt \(\dfrac{x}{2015}=\dfrac{y}{2016}=\dfrac{z}{2017}=k\)

=> x = 2015k ; y = 2016k ; z = 2017k

Khi đó:

\(\left(x-z\right)^3:[\left(x-y\right)^2\left(y-z\right)]\)

= \(\left(2015k-2017k\right)^3:[\left(2015k-2016k\right)^2\left(2016k-2017k\right)]=\left(-2k\right)^3:[\left(-1k\right)^2\left(-1k\right)]=-8k^3:\left(-k\right)^3=8\)