已知X=根号2-1分之根号2+1,Y=根号3+1分之根号3-1，求X的平方-Y的平方

x=(根号2+1）/(根号2-1）=（根号2+1）^2/【(根号2-1）（根号2+1）】=（2+1+2根号2）/(2-1)=3+2根号2

同理得:
y=(根号3-1)^2/(根号3-1)(根号+1)=(3+1-2根号3)/(3-1)=2-根号3

X^2-Y^2=(3+2根号2)^2-(2-根号3)^2
=9+12根号2+8-(4+3-4根号3)
=10+12根号2+4根号3

X=根号2-1分之根号2+1,
x^2 =3+2根号2 (上下同时乘以根号2+1)
Y=根号3+1分之根号3-1
y^2 =1-根号3 (上下同时乘以根号3-1)

所以 x^2-y^2 =3+2根号2-(1-根号3)
=2+ 2根号2+根号3