urak
幼苗
共回答了11个问题采纳率：72.7% 举报
a^3+b^3+3ab=1 (a+b)^3+3ab=1+3ab(a+b) (a+b)^3-1=3ab(a+b-1) (a+b-1)[(a+b)^2+(a+b)+1]=3ab(a+b-1) (a+b-1)[(a+b)^2+(a+b)-3ab+1]=0 (a+b-1)[1/2(a+1)^2+1/2(b+1)^2+1/2(a-b)^2]=0a+b=1,或a=b=-1故a+b=1或a+b=-2
1年前
追问
2
![]()
hyb927
举报
[(a+b)^2+(a+b)-3ab+1]不等于[1/2(a+1)^2+1/2(b+1)^2+1/2(a-b)^2]吧！
![]()
举报
urak
[(a+b)^2+(a+b)-3ab+1]=a²+b²+a+b-ab+1 =1/2(2a²+2a+1+2b²+2b+1-2ab) =1/2(a²+2a+1+b²+2b+1+a²+b²-2ab) =1/2[(a+1)²+(b+1)²+(a-b)²]
赞
