Bài 5:
\(x=by+cz;y=ax+cz\)
\(\Rightarrow x-y=by+cz-\left(ax-cz\right)=by-ax\)
\(\Rightarrow x+ax-y-by=0\)
\(\Rightarrow x\left(a+1\right)=y\left(b+1\right)\)
\(\Rightarrow a+1=\dfrac{y\left(b+1\right)}{x}\)
\(y=ax+cz;z=ax+by\)
\(\Rightarrow y-z=ax+cz-\left(ax+by\right)\)
\(\Rightarrow y-z=cz-by\)
\(\Rightarrow y+by-z-cz=0\)
\(\Rightarrow y\left(b+1\right)=z\left(c+1\right)\)
\(\Rightarrow c+1=\dfrac{y\left(b+1\right)}{z}\)
\(\dfrac{1}{1+a}+\dfrac{1}{1+b}+\dfrac{1}{1+c}=\dfrac{1}{\dfrac{y\left(b+1\right)}{x}}+\dfrac{1}{b+1}+\dfrac{1}{\dfrac{y\left(b+1\right)}{z}}=\dfrac{x}{y\left(b+1\right)}+\dfrac{y}{y\left(b+1\right)}+\dfrac{z}{y\left(b+1\right)}=\dfrac{x+y+z}{y\left(b+1\right)}=\dfrac{2\left(ax+by+cz\right)}{by+y}=\dfrac{2\left(ax+by+cz\right)}{by+ax+cz}=2\)