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？

显示全部楼层 · 2012-4-2 16:13:21

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

千问 · 2012-4-2 16:13:21

解: (x+y-5)2+(z-x-12)2+(y-z-15)2=0 因为(x+y-5)2,(z-x-12)2和(y-z-15)2三者都为非负数则当且仅当(x+y-5)2=0时等式成立
(z-x-12)2=0 ...

千问 · 2012-4-2 16:13:21

∵(x+y-5)平方+(z-x-12)平方+(y-z-15)平方=0∴x+y-5=0z-x-12=0y-z-15=0相加得：2y=35y=16x=-11z=1∴x+y+z=-11+16+1=6...