Solution: | 1 | According to Vieta's theorem, m+n = 2 and m n = | 20 1 1.

|m-n|=√[﹙m+n﹚？ -4mn]=√﹙2？ +8044﹚=4√503.

﹙2﹚m？ -20 1 1m-2009n=﹙m？ -2m﹚-2009﹙m+n﹚=20 1 1-40 18=﹣20 17；

﹙3﹚∵m？ -3m-20 13=m？ -2m-m-20 13=20 1 1-m-20 13=﹣m-2

Similarly: n? -2n-20 13=﹣n-2

∴ (m？ -3m-20 13)(n？ -3n-20 13)=﹙﹣m-2﹚﹙﹣n-2﹚=mn-2﹙m+n﹚+4=2+4022+4=4030.