已知x+y=-5,(x-y)²=1,求3xy与x²+y²-xy的值

已知x+y=-5,(x-y)²=1,求3xy与x²+y²-xy的值
已知x+y=-5,(x-y)²=1,求3xy与x²+y²-xy的值

已知x+y=-5,(x-y)²=1,求3xy与x²+y²-xy的值
x+y=-5,则（x+y）^2=25=x^2+y^2+2xy
(x-y)²=1=x^2+y^2-2xy
两式相减
4xy=24
xy=6
则3xy=18
则x^2+y^2=13
则x^2+y^2-xy=7

(x-y)²
=(x+y)²-4xy
=（-5）²-4xy=25-4xy=1
4xy=24
xy=6
3xy=18
x²+y²-xy
=（x-y）²+xy
=1+6
=7

(x+y)²-(x-y)²＝4xy＝24∴3xy=18∴x²+y²-xy=(x-y)²+xy=7