(2^(1/3)-1)^1/3=a^(1/3)+b^(1/3)+c^(1/3)其中a,b,c皆為有理數,問a,b,c為何?
翻譯: 2開立方根減一再開立方根等於a開立方根加b開立方根加c開立方根
關於立方根難題請數學高手幫忙
2010-11-02 8:19 pm
回答 (2)
2010-11-02 11:28 pm
✔ 最佳答案
[2^(1/3)+1]^3=2+3*4^(1/3)+3*2^(1/3) +1= 3[ 4^(1/3)+ 2^(1/3) +1]= 3/[2^(1/3) -1]
得 [2^(1/3)-1]= 3/[2^(1/3)+1]^3 = [4^(1/3)- 2^(1/3) +1]^3 /9
[2^(1/3) -1]^(1/3)= [ 4^(1/3) -2^(1/3) +1] / 9^(1/3)
= (4/9)^(1/3)- (2/9)^(1/3) + (1/9)^(1/3)
故a+b+c=(4/9)-(2/9)+(1/9)= 1/3
2010-11-02 11:25 pm
1. 三個未知數, 所以應該有三條方程式
2. (2^(1/3)-1)^1/3 = 0.086640349964958, 所以再給兩條方程式, 就可以解出a,b,c
2. (2^(1/3)-1)^1/3 = 0.086640349964958, 所以再給兩條方程式, 就可以解出a,b,c
收錄日期: 2021-04-11 18:27:17
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https://hk.answers.yahoo.com/question/index?qid=20101102000010KK02382