Question

已知X+Y=3，xy=1 ，(1)求X2+Y2的值 （2）求X-Y的值

Answer 1

x²+y²=(x+y)²-2xy=3²-2=9-2=7
(x-y)²=(x+y)²-4xy=3²-4=5
x-y=√5或x-y=-√5

Answer 2

x²+y²
=x²+2xy+y²-2xy
=(x+y)²-2xy
=3²-2=7

(x-y)²=x²-2xy+y²=x²+y²-2xy=7-2=5
∴x-y=±√5