Question

x1/2+x-1/2=3,求(x3/2+x-3/2+2)/ (x-1+x+3)的值

不好意思，不知看不看的懂，有些打不出 X½＋x－½=3,求（(x½)³+ (x－½)³+2）/(x－¹+x+3) ，（x½）³为x的2分之3次方，后面也差不多 我的答案是13/6,对吗！

Answer 1

x1/2+x-1/2=3两边平方得
x+1/x=7，
x3/2+x-3/2=(x1/2+x-1/2)(x+1/x-1)
=3×6=18,
所以(x3/2+x-3/2+2)/ (x-1+x+3)
=20×10=200.

Answer 2

设X½=t
t+1/t=3
t²+1=3t
t²-3t+1=0
t=(3±√5)/2

（(x½)³+ (x－½)³+2）/(x－¹+x+3)
=(t³+1/t³+2)/(t²+1/t²+3)
=[(t+1/t)³-3(t+1/t)+2]/[(t+1/t)²-2+3]
=(3³-3×3+2)/(3²-2+3)
=20/10
=2