问题 填空题
已知(x+
x2+2010
)(y+
y2+2010
)=2010
,则x2-3xy-4y2-6x-6y=______.
答案

(x+

x2+2010
)(y+
y2+2010
)=2010

y+

y2+2010
=
2010
(x+
x2+2010
)
=
2010(
x2+2010
-x)
2010
=
x2+2010
-x

同理x+

x2+2010
=
y2+2010
-y.

两式相加可得x+y=0.

则x2-3xy-4y2-6x-6y=(x+y)(x-4y)-6(x+y)=0.

故答案是:0.

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