請問各位這要怎麼證明啊!!! 設a,b為異於0的實數,且a^3=b^3 則a=b?
回答 (2)
2015-10-18 4:11 pm
a^3=b^3
a^3/b^3=1
a/b=1
a=b
a^3/b^3=1
a/b=1
a=b
2015-10-18 12:35 pm
Sol
a^3=b^3
a^3－b^3=0
(a－b)(a^2+ab+b^2)=0
(a－b)[a^2+2*a*(b/2)+b^2/4+3b^2/4]=0
(a-b)[(a+b/2)^2+3b^2/4]=0
(a+b/2)^2+3b^2/4>0
So
a－b=0
a=b
a^3=b^3
a^3－b^3=0
(a－b)(a^2+ab+b^2)=0
(a－b)[a^2+2*a*(b/2)+b^2/4+3b^2/4]=0
(a-b)[(a+b/2)^2+3b^2/4]=0
(a+b/2)^2+3b^2/4>0
So
a－b=0
a=b
收錄日期: 2021-04-30 20:11:01
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20151018040737AAPihB7