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的平方快

Question

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
快

Answer 1

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