已知(2011+y-x)(x-y-2009)=-2010,求(2011+y-x)²+(2009+y-x)²的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/05 21:35:43
已知(2011+y-x)(x-y-2009)=-2010,求(2011+y-x)²+(2009+y-x)²的值
x){}K5 +u+45*t+u ,5m <؄W+.-0)Ax>i"}*_`gC W3 @IX¥^h Sd S|dD]0$vn~6m'qQbvmk/jmMekb`db_\g ^0Ht*b㌴ DX#

已知(2011+y-x)(x-y-2009)=-2010,求(2011+y-x)²+(2009+y-x)²的值
已知(2011+y-x)(x-y-2009)=-2010,求(2011+y-x)²+(2009+y-x)²的值

已知(2011+y-x)(x-y-2009)=-2010,求(2011+y-x)²+(2009+y-x)²的值
(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

(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