Question

已知x,y,z,满足1/2|x-y|+根号下（2y+z）+z^2-z+1/4=0,求（x+z)^2

Answer 1

1/2|x-y|≥0 √（2y+z）≥0 z^2-z+1/4=（z-0.5)^2≥0
又因为和为0,所以三项都为0,
所以x=y 2y+z=0 z=0.5 2y=-0.5 y=-0.25 x=-0.25
（x+z)^2=0.25^2=1/16