Question

已知x-y+3的绝对值与2(x+y)的平方互为相反数,求x的平方+2xy+y的平方的值

Answer 1

∵x-y+3的绝对值与2(x+y)的平方互为相反数

即│x-y+3│=-4(x+y)²==>│x-y+3│+4(x+y)²=0

∴x+y=0,x-y+3=0

故x的平方+2xy+y的平方=x²+2xy+y²

=(x+y)²

=0²

=0