问题
填空题
若知|x1-1|+(x2-2)2+|x3-3|3+…+|x2011-2011|2011+(x2012-2012)2012=0, 则
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答案
根据题意得:x1-1=0,x2-2=0,x3-3=0,…x2011-2011=0,x2012-2012=0.
解得:x1=1,x2=2,x3=3,…,x2011=2011,x2012=2012.
则
+1 x1x2
+1 x2x3
+…+1 x3x4 1 x2011x2012
=
-1 x1
+1 x2
-1 x2
+…+1 x3
-1 x 2011 1 x2012
=
-1 x1 1 x2012
=1-1 2012
=
.2011 2012
故答案是:
.2011 2012