若(x+y)(x+y-2)=24,则x+y的值为_.

问题描述:

若(x+y)(x+y-2)=24,则x+y的值为______.

设t=x+y,则原方程可化为:t(t-2)=24,则t2-2t-24=0,即(t-6)(t+4)=0
∴t=6或-4,即x+y=6或-4
故答案是:6或-4.