已知实数a、b、c满足1/2|a-b|+根号2b+c+c²-c+1/4=0,求a(b+c)的值

1/2|a-b|≥0
√(2b+c)≥0
c²-c+1/4=(c-1/2)²≥0
1/2|a-b|+√(2b+c)+c²-c+1/4=(c-1/2)²=0
∴1/2|a-b|=0√(2b+c)=0(c-1/2)²=0
∴a-b=0
2b+c=0
c-1/2=0
∴a=-1/4 b=-1/4 c=1/2 a(a+b)=-1/16