x+1/x=5，問x^2/x^4+x^2+1=? ANS:1/24...點計?
回答 (2)
2007-11-29 4:57 am
✔ 最佳答案
x+1/x=5(x+1/x)^2=5^2
x^2+2+1/x^2=25
1/x^2+x^2+1+1=25
x^2/(x^2*x^2)x^2+1+=24
x^2/x^4+x^2+1=24
你條式好亂,我睇唔明,下次加( ),易睇d
參考: me
2007-11-29 5:31 am
x + 1 / x = 5
x^2 - 5x + 1 = 0
用二次公式:
x = ( 5 + sqr 21)/ 2 or ( 5 - sqr 21 ) / 2
x^2/(x^4+x^2+1)
= [( 5 + sqr 21)/ 2]^2 / [( 5 + sqr 21)^4/ 16 + ( 5 + sqr 21)^2/ 4 + 1 ]
= 1 / 24
或
x^2/(x^4+x^2+1)
= [( 5 - sqr 21)/ 2]^2 / [( 5 - sqr 21)^4/ 16 + ( 5 - sqr 21)^2/ 4 + 1 ]
= 1 / 24
所以ans: 1 / 24
x^2 - 5x + 1 = 0
用二次公式:
x = ( 5 + sqr 21)/ 2 or ( 5 - sqr 21 ) / 2
x^2/(x^4+x^2+1)
= [( 5 + sqr 21)/ 2]^2 / [( 5 + sqr 21)^4/ 16 + ( 5 + sqr 21)^2/ 4 + 1 ]
= 1 / 24
或
x^2/(x^4+x^2+1)
= [( 5 - sqr 21)/ 2]^2 / [( 5 - sqr 21)^4/ 16 + ( 5 - sqr 21)^2/ 4 + 1 ]
= 1 / 24
所以ans: 1 / 24
參考: My Maths Knowledge
收錄日期: 2021-04-29 19:58:32
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