Question

Cho x,y,z khác 0 và x-y-z=0,tính giá trị biểu thức

 B= (1 - z/x) (1- x/y) (1+ y/z)

Answer 1

x - y - z = 0

x = y + z

y = x - z

z = x - y => -z = y - x

B = (1 - z/x)(1 - x/y) (1 + y/z)

B = (x/x - z/x)( y/y - x/y) ( z/z + y/z)

B = \(\frac{x-z}{x}\cdot\frac{y-x}{y}\cdot\frac{z+x}{z}=\frac{y}{x}\cdot\frac{-z}{y}\cdot\frac{x}{z}=-1\)

 

Answer 2

x - y - z = 0

x = y + z

y = x - z

z = x - y => -z = y - x

B = (1 - z/x)(1 - x/y) (1 + y/z)

B = (x/x - z/x)( y/y - x/y) ( z/z + y/z)

B = \(\frac{x - z}{x} \cdot \frac{y - x}{y} \cdot \frac{z + x}{z} = \frac{y}{x} \cdot \frac{- z}{y} \cdot \frac{x}{z} = - 1\)