1.(5＋根号6＋根号10＋根号15)/(根号2＋根号3＋根号5 )
=(根号6＋根号10＋根号15+根号25)/(根号2＋根号3＋根号5
=(根号6＋根号5(根号2＋根号3＋根号5 )/(根号2＋根号3＋根号5 )
=根号6/(根号2＋根号3＋根号5)+ 根号5
=[根号6*(根号5-根号3-根号2)]/(根号2＋根号3＋根号5)*(根号5-根号3-根号2)+ 根号5
=(根号5+根号3+根号2)/2
2.x²+y²+x+y=18 (1)
x²+xy+y²=19 (2)
(2)-(1)
XY-(X+Y)=1
x+y=xy-1 (3)
由（1）得
(x+y)^2+(x+y)-2xy=18 (4)
把（3）代入（4）得
(xy-1)^2+(xy-1)-2xy=18
设xy=k
(k-1)^2+(k-1)-2k=18
k^2-3k-18=0
则k=6或-3
即xy=6或-3
x+y=5或-4
可解得x.y