已知x+y=3 xy=2则x²-y²的值

已知x+y=3 xy=2则x²-y²的值
已知x+y=3 xy=2则x²-y²的值

已知x+y=3 xy=2则x²-y²的值
x+y=3
(x+y)²=9
x²+2xy+y²=9
x²-2xy+y²=9-4xy
(x-y)²=9-8
x-y=±1
∴x²-y²=(x+y)(x-y)=3×(±1)=±3

∵x+y=3 ∴y=3-x ∵xy=2 ∴x（3-x）=2 解得：x1=1 x2=2 ∴：y1=2 y2=1 故x²-y²=1-4=-3/4-1=3
不确定0.0

(x-y)²=(x+y)²-4xy=1 x²-y²=(x+y)(x-y)=3或者-3