Question

giúp mk câu này vs

Cho x,y,z ≠ 0 và x-y-z = 0 . Tính

A=(1-\(\dfrac{z}{x}\))(1-\(\dfrac{x}{y}\))(1+\(\dfrac{y}{z}\))

Answer 1

Có \(x-y-z=0\)
\(\Rightarrow\left\{{}\begin{matrix}x-z=y\\x-y=z\\z+y=x\end{matrix}\right.\Rightarrow y-x=-z\)
Có x,y,z ≠ 0
\(\Rightarrow A=\left(1-\dfrac{z}{x}\right)\left(1-\dfrac{x}{y}\right)\left(1+\dfrac{y}{z}\right)\)
\(\Rightarrow A=\left(\dfrac{x-z}{x}\right)\left(\dfrac{y-x}{y}\right)\left(\dfrac{z+y}{z}\right)\)
\(\Rightarrow A=\left(\dfrac{y}{x}\right)\left(\dfrac{-z}{y}\right)\left(\dfrac{x}{z}\right)\)
\(\Rightarrow A=1\)
Vậy A = 1

Answer 2

A = -1
/ ấn nhầm ~ xin lỗi /
Vậy A = -1