问题 解答题

化简求值:若4x2+4x+y2-6y+10=0,试求(x2+2y2+3)(x2+2y2-3)-(x-2y)2(x+2y)2的值.

答案

∵4x2+4x+y2-6y+10=0,

∴4x2+4x+1+y2-6y+9=0,

∴(2x+1)2+(y-3)2=0,

∴2x+1=0,y-3=0,

∴x=-

1
2
,y=3,

∴原式=(x2+2y22-9-(x2-4y22

=(x2+2y2+x2-4y2)(x2+2y2-x2+4y2)-9

=6y2×(2x2-2y2)-9

=12y2(x2-y2)-9

=12×9×(-

35
4
)-9

=-995-9

=-1004.

多项选择题
填空题