如果 x^2－3x＋1＝0 ,求 x^2＋1/(x^2)

x^2＋1/(x^2)=(x+1/x)^2-2

现在来求x+1/x，
x^2－3x＋1＝0，两边同除x得到，
x-3+1/x=0 得到x+1/x=3代入上面得到

x^2＋1/(x^2)=(x+1/x)^2-2=7

x^2－3x＋1＝0
===>x=(3±√5)/2
===>x^2=[(3±√5)/2]^2=(7±3√5)/2
===>1/x^2=(7±3√5)/2<±号与上边相反>
===>x^2＋1/(x^2)=7

x^2-3x+1=0
x-3+1/x=0
x+1/x=3
x^2+2+1/x^2=9
x^2+1/x^2=7