已知x+y=3,xy=1,求:(1)x²+y²(2)(x-y)²的值

已知x+y=3,xy=1,求:(1)x²+y²(2)(x-y)²的值
已知x+y=3,xy=1,求:(1)x²+y²(2)(x-y)²的值

已知x+y=3,xy=1,求:(1)x²+y²(2)(x-y)²的值
（1）x²+y²=(x+y)²-2xy
=9-2
=7
(2）(x-Y)²=x²-2xy+y²
=7-2xy
=7-2
=5

解
x+y=3
两边平方
x²+y²+2xy=9
∵xy=1
∴x²+y²+2=9
∴x²+y²=7

(x-y)²
=(x+y)²-4xy
=3²-4×1
=9-4
=5