已知x=(√2+1)/(√2-1),y=(√2-1)/(√2+1),求x2-y2的值和y/x＋x/y的值
问题描述：
已知x=(√2+1)/(√2-1),y=(√2-1)/(√2+1),求x2-y2的值和y/x＋x/y的值
答
x=(根号2＋1）＾2／(2－1)＝2＋1＋2根号2＝3＋2根号2
Y＝(根号2－1)＾2／(2－1)＝2+1-2根号2＝3－2根号2
x^2-y^2=(x+y)(x-y)=6*4根号2＝24根号2
y/x+x/y=(x^2+y^2)/xy=[(x+y)^2-2xy]/xy=(x+y)^2/xy-2=6^2/(9-8)-2=34