已知非零实数a,b,c满足a+b+c=0,求证a3+b3+c3=3abc

2025-03-04 13:59:55
推荐回答(2个)
回答1:


回答2:

a³+ b³+ c³
=(a³+b³) + c³
=(a+b)(a²-ab+b²) +c³
=-c(a²+2ab +b² -3ab) + c³
=-c[(a+b)²-3ab] + c³
=-c[(-c)² -3ab) + c³
=-c³ + 3abc + c³
=3abc