Vì : \(ƯCLN\left(a,b\right)=9\Rightarrow\left\{\begin{matrix}a=9.k_1\\b=9.k_2\end{matrix}\right.\) với \(ƯCLN\left(k_1,k_2\right)=1\)
Thay vào : \(a+b=90\) ta có :
\(9.k_1+9.k_2=90\Rightarrow9\left(k_1+k_2\right)=90\Rightarrow k_1+k_2=10\)
+) Nếu : \(k_1=1;k_2=9\Rightarrow\left\{\begin{matrix}a=9.1=9\\b=9.9=81\end{matrix}\right.\)
+) Nếu : \(k_1=3;k_2=7\Rightarrow\left\{\begin{matrix}a=9.3=27\\b=9.7=63\end{matrix}\right.\)
Vậy a = 9 thì b = 81
a = 27 thì b = 63