已知(2011+y-x)(x-y-2009)=－2010,求(2011+y-x)²+(2009+y-x)²的值
问题描述：
已知(2011+y-x)(x-y-2009)=－2010,求(2011+y-x)²+(2009+y-x)²的值
答
(2011+y-x)²+(2009+y-x)²
=[(2011+y-x)-(2009+y-x)]^2+2*(2011+y-x)(2009+y-x)
=2^2+2*2010
=4024
答
(2011+y-x)(x-y-2009)=－2010
-(2011+y-x)(2009+y-x)=－2010
(2011+y-x)(2009+y-x)==2010
令a=2011+y-x,b=2009+y-x
所以a-b=2
平方
a²-2ab+b²=4
所以(2011+y-x)²+(2009+y-x)²
=4+2ab
=4+2×2010
=4024