Question

若根号x-2y+9与x-y-3的绝对值互为相反数,则x+y的值为

Answer 1

算术平方根与绝对值项均恒非负,两者互为相反数,只有0的相反数是0,都非负,因此

x-2y+9=0 (1)

x-y-3=0 (2)

(2)-(1)

y-12=0

y=12

代入(2)

x=y+3=12+3=15

x=15 y=12