a) Vì \(a_1+a_2+......+a_9\ne0\)
\(\Rightarrow\)Ta có: \(\frac{a_1}{a_2}=\frac{a_2}{a_3}=.........=\frac{a_8}{a_9}=\frac{a_9}{a_1}=\frac{a_1+a_2+......+a_8+a_9}{a_2+a_3+......+a_9+a_1}=1\)
\(\Rightarrow a_1=a_2\); \(a_2=a_3\); ........... ; \(a_8=a_9\); \(a_9=a_1\)
\(\Rightarrow a_1=a_2=a_2=........=a_9\)( đpcm )