根号x-y+3与根号x+y-1互为相反数求x+y

Question

根号x-y+3与根号x+y-1互为相反数求x+y

Answer 1

√(x-y+3)与√(x+y-1)互为相反数求x+y
因为√(x-y+3)与√(x+y-1)互为相反数,∴√(x-y+3)+√(x+y-1)=0；而√(x-y+3)与√(x+y-1)都是非
负数,两个非负数之和为零,那只有两个数都是零才有可能,故必有：
x-y+3=0.(1)
x+y-1=0.(2)
(1)+(2)得2x+2=0,故x=-1,代入(1)式即得y=2,故x+y=-1+2=1 .