Question

已知(x+y-5)平方+(z-x-12)平方+(y-z-15)平方=0,那么x+y+z=多少?

Answer 1

(x+y-5)平方+(z-x-12)平方+(y-z-15)平方=0

由非负性

x+y-5=0.(1)

z-x-12=0.(2)

y-z-15=0.(3)

解

(2)+(3)得

y-x=27

联立(1)得

x=-11

y=16

z=1

x+y+z=-11+16+1=6