x+y=2,且【x+2】【y+2】=5,求x^2+xy+y^2的值

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x+y=2,且【x+2】【y+2】=5,求x^2+xy+y^2的值
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x+y=2,且【x+2】【y+2】=5,求x^2+xy+y^2的值
x+y=2,且【x+2】【y+2】=5,求x^2+xy+y^2的值

x+y=2,且【x+2】【y+2】=5,求x^2+xy+y^2的值
(x+y=2)
(x+2)(y+2)=xy+2(x+y)+4 = 5
所以xy= -3
(x^2+xy+y^2)=(x+y)^2-xy = 4+3 = 7

(x+y)^2=x^2+2xy+y^2=4
【x+2】【y+2】=xy+2(x+y)+4=5 xy=5-4-2(x+y)=-3
x^2+xy+y^2=(x+y)^2-xy=4-(-3)=7