作业帮小明在计算20112009^2+20112011^2-2分之20112010^2时,找不到计算器,于是去向小敏借,小敏看了看题目说,根本不需要计算器,并且很快说出了答案,你知道她是怎样做的吗?
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小明在计算20112009^2+20112011^2-2分之20112010^2时,找不到计算器,于是去向小敏借,小敏看了看题目说,根本不需要计算器,并且很快说出了答案,你知道她是怎样做的吗?
小明在计算20112009^2+20112011^2-2分之20112010^2时,找不到计算器,于是去向小敏借,小敏看了看题目说,根本不需要计算器,并且很快说出了答案,你知道她是怎样做的吗?
小明在计算20112009^2+20112011^2-2分之20112010^2时,找不到计算器,于是去向小敏借,小敏看了看题目说,根本不需要计算器,并且很快说出了答案,你知道她是怎样做的吗?
20112009^2+20112011^2-2*20112010^2
=(20112010-1)^2+(20112010+1)^2-2*20112010^2
=20112010^2-40224020+1+20112010^2+40224020+1-2*20112010^2
=2*20112010^2+2-2*20112010^2
=2
2分之20112010^2 这是啥玩意儿啊 小朋友
20112009^2+20112011^2-2分之20112010^2=(20112010-1)^2+(20112010+1)^2-2分之20112010^2=20112010^2-2*20112010+1+20112010^2+2*20112010+1-2分之20112010^2=20112010^2*2分之20112010^2=0.5
Let x = 20112010, then your question of 20112009^2+20112011^2-2分之20112010^2 becomes:
(x-1)^2 + (x+1)^2 - 0.5*x^2, which can be expanded and simplified:
= (x^2 - 2x + 1) + (x^2 + 2x + 1) - 0.5x...
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Let x = 20112010, then your question of 20112009^2+20112011^2-2分之20112010^2 becomes:
(x-1)^2 + (x+1)^2 - 0.5*x^2, which can be expanded and simplified:
= (x^2 - 2x + 1) + (x^2 + 2x + 1) - 0.5x^2
= 1.5x^2 + 2
At this point, we know your original problem is wrong. To make this problem easily done without a calculator, you really needed it to say:
"小明在计算20112009^2+20112011^2-2*20112010^2时", not 2分之 something.
That way you'd have, instead:
(x-1)^2 + (x+1)^2 - 2*x^2, which can be expanded and simplified:
= (x^2 - 2x + 1) + (x^2 + 2x + 1) - 2x^2
= 2
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