问题
解答题
已知ax2+bx+1与2x2-3x+1的积不含x3和x项，试计算下面代数式的值．
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答案
（ax2+bx+1）•（2x2-3x+1），
=2ax4-3ax3+ax2+2bx3-3bx2+bx+2x2-3x+1，
=2ax4+（-3a+2b）x3+（a-3b+2）x2+（b-3）x+1，
∵不含x3和x项，
∴b-3=0，-3a+2b=0，
∴b=3，a=2，
把a=2，b=3代入得：
+1 (a-1)(b-1)
+1 ab
+1 (a+1)(b+1)
+…+1 (a+2)(b+2) 1 (a+2010)(b+2010)
=
+1 1×2
+1 2×3
+1 3×4
+…+1 4×5 1 2012×2013
=
-1 1
+1 2
-1 2
+1 3
-1 3
+1 4
-1 4
+…+1 5
-1 2012 1 2013
=1-1 2013
=
．2012 2013