Áp dụng tính chất dãy tỉ số bằng nhau ta có : 

\(\frac{x_1-1}{3}=\frac{x_2-2}{2}=\frac{x_3-3}{1}=\frac{\left(x_1-1\right)+\left(x_2-2\right)+\left(x_3-3\right)}{3+2+1}=\frac{\left(x_1+x_2+x_3\right)-6}{6}=\frac{30-6}{6}=\frac{24}{6}=4\)

=> \(\frac{x_1-1}{3}=4\Rightarrow x_1=13\)

     \(\frac{x_2-2}{2}=4\Rightarrow x_2=10\)

     \(\frac{x_3-3}{1}=4\Rightarrow x_3=7\)

=> \(x_1.x_2-x_2.x_3=13.10-10.7=10\left(13-7\right)=10.6=60\)

Vậy   \(x_1.x_2-x_2.x_3=60\)