Question

奥数题：2007.7x2007.6-2006.6x2006.7=

Answer 1

2007.7×2007.6－2006.6×2006.7
＝2007.7×(2006.6＋1)－2006.6×2006.7
＝2007.7×2006.6＋2007.7×1－2006.6×2006.7
＝(2007.7－2006.7)×2006.6＋2007.7
＝1×2006.6＋2007.7
＝2006.6＋2007.7
＝4014.3

Answer 2

2007.7X2007.6-2006.6X2006.7
=2007.7X2007.6-（2007.7-1）X2006.6
=2007.7X2007.6-2007.7X2006.6+2006.6
=2007.7（2007.6-2006.6）+2006.6
=2007.7+2006.6
=4014.3。

Answer 3

2007.7x2007.6-2006.6x2006.7
=(2008-0.3)*(2008-0.4)-(2007-0.3)(2007-0.4)
=2008^2-0.7*2008+0.12-(2007^2-0.7*2007+.012)
=2008^2-2007^2-0.7*(2008-2007)
=(2008+2007)(2008-2007)-0.7
=4015-0.7
=4014.3

Answer 4

=(2008-0.3)*(2008-0.4)-(2007-0.3)(2007-0.4)
=2008*2008-0.7*2008+0.12-2007*2007+0.7*2007-0.12
=(2008+2007)*(2008-2007)-0.7(2008-2007)
=4014.3

Answer 5

消元法，设2007.7为a，2007.6为b，
=ab-(b-1)(a-1)
=ab-ab+b+a-1
=b+a-1
=2007.7+2007.6-1
=4015.3-1
=4014.3