x+1/x=5，問x^2/x^4+x^2+1=? ANS:1/24...點計?

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

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