問題如下:
1=2??
Proof:
Set: x=y
x^2=xy
x^2-y^2=xy-y^2
(x+y)(x-y)=y(x-y)
x+y=y
y=y+y
y=2y
Sub:y=1
1=2??
Any mistake in this proof??
呢條式有冇錯呢?
如有，咁錯係邊呢??
我覺得呢條問題幾有趣，所以俾大家諗下。最快又最準果位可得到知識點10*2分= =
開放3天= =
我諗呢一題適合中二或以上既人作答
一條有趣的數學問題
2008-02-14 1:06 am
回答 (3)
2008-02-14 1:33 am
✔ 最佳答案
當然有錯。首先，最直接的︰
y=2y
則 y-y=2y-y
y=0
[y=2y 是未完成 不可妄然sub數]
第二，在這一步︰
(x+y)(x-y)=y(x-y)
不應就此「若」去terms 變成 x+y=y
而應該︰
(x+y)(x-y) - y(x-y)=0
Factorize,
(x+y-y)(x-y)=0
x(x-y)=0
則
x=0 or x=y
若x=0, y=0 (由於x=y)
hope this helps u =]
2008-02-14 1:39 am
所有既一元二次方程式,都會有一個或者兩個既答案可能,你無端端兩邊都一齊eliminate左(x-y).....=>
(x+y)(x-y)=y(x-y)
x+y=y
咪錯左囉~~~~~~
(x+y)(x-y)=y(x-y)
x+y=y
咪錯左囉~~~~~~
2008-02-14 1:18 am
As x-y=0, thus (x+y)(x-y)=y(x-y) <=/=> x+y=y
收錄日期: 2021-04-14 00:06:14
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080213000051KK03060