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?](/uploads/image/z/2831679-63-9.jpg?t=%E5%B0%8F%E6%98%8E%E5%9C%A8%E8%AE%A1%E7%AE%9720112009%5E2%2B20112011%5E2-2%E5%88%86%E4%B9%8B20112010%5E2%E6%97%B6%2C%E6%89%BE%E4%B8%8D%E5%88%B0%E8%AE%A1%E7%AE%97%E5%99%A8%2C%E4%BA%8E%E6%98%AF%E5%8E%BB%E5%90%91%E5%B0%8F%E6%95%8F%E5%80%9F%2C%E5%B0%8F%E6%95%8F%E7%9C%8B%E4%BA%86%E7%9C%8B%E9%A2%98%E7%9B%AE%E8%AF%B4%2C%E6%A0%B9%E6%9C%AC%E4%B8%8D%E9%9C%80%E8%A6%81%E8%AE%A1%E7%AE%97%E5%99%A8%2C%E5%B9%B6%E4%B8%94%E5%BE%88%E5%BF%AB%E8%AF%B4%E5%87%BA%E4%BA%86%E7%AD%94%E6%A1%88%2C%E4%BD%A0%E7%9F%A5%E9%81%93%E5%A5%B9%E6%98%AF%E6%80%8E%E6%A0%B7%E5%81%9A%E7%9A%84%E5%90%97%3F)
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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