已知x+y=-5,(x-y)²=1,求3xy与x²+y²-xy的值
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![已知x+y=-5,(x-y)²=1,求3xy与x²+y²-xy的值](/uploads/image/z/2668713-33-3.jpg?t=%E5%B7%B2%E7%9F%A5x%2By%3D-5%2C%28x-y%29%26%23178%3B%3D1%2C%E6%B1%823xy%E4%B8%8Ex%26%23178%3B%2By%26%23178%3B-xy%E7%9A%84%E5%80%BC)
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