Question

[Trương Tuấn Kiệt]

 Cho 3 số x;y;z \(\ne\)0 thỏa mãn điều kiện:

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

Khi đó: B = ( 1   +   \(\frac{x}{y}\)) * ( 1    +   \(\frac{y}{z}\)) * ( 1   +  \(\frac{z}{x}\)) = ?

Answer 1

[Đinh Đức Hùng]

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

\(\Leftrightarrow\frac{y+z-x}{x}+2=\frac{z+x-y}{y}+2=\frac{x+y-z}{z}+2\)

\(\Leftrightarrow\frac{x+y+z}{x}=\frac{x+y+z}{y}=\frac{x+y+z}{z}\)

\(\Rightarrow x=y=z\)

\(\Rightarrow\frac{x}{y}=1;\frac{y}{z}=1;\frac{z}{x}=1\)

\(\Rightarrow B=\left(1+1\right)\left(1+1\right)\left(1+1\right)=2^3=8\)