If a^1/2 + a^-1/2 = 3, find the value of a^3/2 + a^-3/2
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2010-11-09 5:08 am
回答 (2)
2010-11-09 5:15 am
✔ 最佳答案
設 y = a^1/2,則y + 1/y = 3
(y + 1/y)^3 = 3^3
y^3 + 3y + 3/y + 1/y^3 = 27
y^3 + 1/y^3 + 3(y + 1/y) = 27
y^3 + 1/y^3 + 3(3) = 27
y^3 + 1/y^3 = 18
a^3/2 + a^-3/2 = 18
2010-11-08 21:16:37 補充：
(y + 1/y)^3
= (y^2 + 2 + 1/y^2)(y + 1/y)
= y^3 + y + 2y + 2/y + 1/y + 1/y^3
= y^3 + 3y + 3/y + 1/y^3
參考: 請勿抄襲
2010-11-09 8:48 pm
a^(3/2) + a^(-3/2)= [a^(1/2)]^3 + [a^(-1/2)]^3= [a^(1/2) + a^(-1/2)] {[a^(1/2)]^2 – [a^(1/2)][a^(-1/2)] + [a^(-1/2)]^2}= 3{[a^(1/2)]^2 - [a^(1/2)][a^(-1/2)] + [a^(-1/2)]^2}= 3{[a^(1/2)]^2 + 2[a^(1/2)][a^(-1/2)] + [a^(-1/2)]^2 - 3[a^(1/2)][a^(-1/2)]}= 3{[a^(1/2) + a^(-1/2)]^2 - 3[a^(1/2)][a^(-1/2)]}= 3{[a^(1/2) + a^(-1/2)]^2 - 3[a^(1/2)][a^(-1/2)]}= 3{[3]^2 - 3[a^(1/2)][a^(-1/2)]}= 3{[3]^2 - 3[1]}= 3{9 - 3}= 18
參考: knowledge
收錄日期: 2021-04-28 14:20:50
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101108000051KK01455