Question

tìm x,y,z biết x/z+y+5=y/x+z+5 = z/x+y-10=x+y+z

Answer 1

Lời giải:

Nếu $x+y+z=0$

$\Rightarrow \frac{x}{z+y+5}=\frac{y}{x+z+5}=\frac{z}{x+y-10}=0$

$\Rightarrow x=y=z=0$

Nếu $x+y+z\neq 0$

Áp dụng TCDTSBN:

$x+y+z=\frac{x}{z+y+5}=\frac{y}{x+z+5}=\frac{z}{x+y-10}=\frac{x+y+z}{z+y+5+x+z+5+x+y-10}=\frac{x+y+z}{2(x+y+z)}=\frac{1}{2}$

$\Rightarrow \frac{z+y+5}{x}=\frac{x+z+5}{y}=\frac{x+y-10}{z}=2$

$\Rightarrow \frac{x+y+z+5}{x}=\frac{x+y+z+5}{y}=\frac{x+y+z-10}{z}=3$

$\Rightarrow \frac{5,5}{x}=\frac{5,5}{y}=\frac{-9,5}{z}=3$

$\Rightarrow x=\frac{11}{6}; y=y=\frac{11}{6}; z=\frac{-19}{6}$