若2|X-Y|+(根号2Y+Z)+Z^2-Z+1/4＝0,求X＋Y＋Z的值．

Question

若2|X-Y|+(根号2Y+Z)+Z^2-Z+1/4＝0,求X＋Y＋Z的值．

Answer 1

2|X-Y|+(根号2Y+Z)+Z^2-Z+1/4＝0
2|X-Y|+(根号2Y+Z)+(Z-1/2)^2＝0
x-y=0,2y+z=0,z-1/2=0
x=y=-1/4,z=1/2
X＋Y＋Z=-1/4-1/4+1/2=0