maths! maths! maths!

2009-08-06 9:09 pm
p. 12
The following work shows that for any two equal numbers a and b, we have 1 = 2. What is wrong in the work?

a = b , ab = b2 , ab-a2 = b2-a2 , a(b-a) - (b+a)(b-a) , a = b+a , a = b+b , a =2b , b = 2b , 1 = 2
更新1:

係吾係有D亂呀?因為吾知why我的電腦一打到ab-a2 = b2-a2就打吾到,如果看不明,只要把上面的數字直寫就可以. e.g. a=b ab=b2 ab-a2=b2-a2 ...

回答 (1)

2009-08-06 9:19 pm
✔ 最佳答案
a = b , ab = b2 , ab-a2 = b2-a2 , a(b-a) = (b+a)(b-a) , a = b+a , a = b+b , a =2b , b = 2b , 1 = 2
問題出在藍色部份。因為a=b,b-a=0﹐兩邊除0在運算上是禁止的﹐故此証明不成立


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