Need help in number theory:

(1) If a is rational, b is irrational, prove that a+b is irrational.

(2) if a is rational, b is irrational, prove that ab is irrational, for a != 0.

 

This is like common sense... How to prove it??

 

hehe，就是因为是common sense，才能体现出数学家孜孜不倦的钻研精神啊～～～～

 

 

用定义直接推就好了

Assume (a+b) is rational, so (a+b)=c/d, where gcd(c,d)=1.
=> (a+b)d=c => c|d
Since gcd(c,d)=1, c!|d
Hence, there is a contradiction in the assumption.
=> (a+b) cannot be expressed in the form c/d. i.e. (a+b) is irrational.


Is my proof correct??

。。。

 

没那么复杂了，我贴了第一题的答案，第二题照着做吧

[ 本帖最后由 k4knight 于 2008-4-10 07:29 PM 编辑 ]

where??

引用:

原帖由 Scoriger 于 2008-4-10 07:28 PM 发表 where??

 

汗，我果然BC

我开始认真复习复习复习

引用:

原帖由 k4knight 于 2008-4-10 06:31 PM 发表   汗，我果然BC

 

 

Thank you!!! you possess great niubility!!!

 

引用:

原帖由 marthanovera 于 2008-4-10 06:40 PM 发表 我开始认真复习复习复习

 

 

Don't worry! this homework is due on monday...

i have not started my revision for tmr's exam! haha...

fan zheng
a/b - c/d
(a/b)/(c/d)