1
√x+1/√x=3
t=√x >0
t+1/t=3
t^2-3t+1=0
(t-3/2)^2=5/4
t=-√5/2+3/2或t=-√5/2+3/2
x=t^2=5/4+9/4-3√5/2=14/4-3√5/2
或x=t^2=14/4+3√5/2
(x+1)/x=1+1/x
1/x=4(14-6√5)/(256-45)=(56+24√5)/211
或1/x=(56-24√5)/211
2
如果是求x+1/x,比较容易
(√x+1/√x)^2=9
x+2+1/x=9
x+1/x=7