已知0<x<1,且x+1/x=5,則x^2-1/x^2之值為何?
回答 (2)
2016-11-01 4:30 am
(x+1)/x=5
x+1=5x
4x=1
x=0.25
(x^2-1)/x^2
=(0.25^2-1)/(0.25)^2
=-3.75
x+1=5x
4x=1
x=0.25
(x^2-1)/x^2
=(0.25^2-1)/(0.25)^2
=-3.75
2016-10-31 7:21 pm
Sol
x+1/x=5
x^2+1=5x
x^2－5x+1=0
x=(5－√21)/2 (正不合)
1/x=2/(5－√21)=(5+√21)/2
X－1/x=－√21
x^2－1/x^2=(x+1/x)(x－1/x)=－5√21
x+1/x=5
x^2+1=5x
x^2－5x+1=0
x=(5－√21)/2 (正不合)
1/x=2/(5－√21)=(5+√21)/2
X－1/x=－√21
x^2－1/x^2=(x+1/x)(x－1/x)=－5√21
收錄日期: 2021-04-18 15:43:46
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20161031070752AALu9oZ