if x= a - (----) ,
aaaaaa a
aaaaaaaaaaaaaaa 1
express (a^3)- (----------)
aaaaaaaaaaaaaa a^3
in terms of a
更新1:
please give steps
rational function question
2012-05-07 2:09 am
a aaaaaa1
if x= a - (----) ,
aaaaaa a
aaaaaaaaaaaaaaa 1
express (a^3)- (----------)
aaaaaaaaaaaaaa a^3
in terms of a
if x= a - (----) ,
aaaaaa a
aaaaaaaaaaaaaaa 1
express (a^3)- (----------)
aaaaaaaaaaaaaa a^3
in terms of a
回答 (4)
2012-05-07 2:28 am
✔ 最佳答案
if x=a－1/a，express a^3－1/a^3，in terms of xSol
a^3－1/a^3
=(a－1/a)(a^2+1+1/a^2)
=(a－1/a)(a^2－2+1/a^2+3)
=x(x^2+3)
2012-05-07 3:29 am
x=a-1/a
x³=a³-3a+3/a-1/a³
a³-1/a³=x³+3a-3/a=x³+3x
x³=a³-3a+3/a-1/a³
a³-1/a³=x³+3a-3/a=x³+3x
2012-05-07 2:36 am
x = a - (1/a)^2
x^2
= [a - (1/a)]^2
= a^2 - 2 + (1/a)^2
= a^2 + (1/a)^2 - 2
so
a^3 - (1/a^3)
= a^3 - (1/a)^3
[by formula a^3 - b^3 = (a - b)(a^2 + ab + b^2)
= [a - (1/a)][a^2 + 1 + (1/a)^2]
= x [a^2 + (1/a)^2 - 2 + 3]
= x (x^2 + 3)
若覺得我幫到你，可否我的 Facebook Page 比個 Like 我？感激！
經數學人 http://fb.com/ronaldchik
x^2
= [a - (1/a)]^2
= a^2 - 2 + (1/a)^2
= a^2 + (1/a)^2 - 2
so
a^3 - (1/a^3)
= a^3 - (1/a)^3
[by formula a^3 - b^3 = (a - b)(a^2 + ab + b^2)
= [a - (1/a)][a^2 + 1 + (1/a)^2]
= x [a^2 + (1/a)^2 - 2 + 3]
= x (x^2 + 3)
若覺得我幫到你，可否我的 Facebook Page 比個 Like 我？感激！
經數學人 http://fb.com/ronaldchik
參考: 經數樂園 http://ronaldchik.blogspot.com
2012-05-07 2:30 am
x = a - 1/a
x^2
= (a - 1/a)^2
= a^2 - 2a(1/a) + 1/a^2
= a^2 + 1/a^2 - 2
a^2 + 1/a^2 = x^2 + 2
a^3 - 1/a^3
= (a - 1/a)(a^2 + (a)(1/a) + 1/a^2)
= (a - 1/a)(a^2 + 1/a^2 + 1)
= x(x^2 + 2 + 1)
= x(x^2 + 3)
x^2
= (a - 1/a)^2
= a^2 - 2a(1/a) + 1/a^2
= a^2 + 1/a^2 - 2
a^2 + 1/a^2 = x^2 + 2
a^3 - 1/a^3
= (a - 1/a)(a^2 + (a)(1/a) + 1/a^2)
= (a - 1/a)(a^2 + 1/a^2 + 1)
= x(x^2 + 2 + 1)
= x(x^2 + 3)
參考: myself
收錄日期: 2021-04-26 21:13:44
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120506000051KK00565