Question

Cho a+b+c=0. Chứng minh a³+b³+c³=abc

Answer 1

a³ + b³ + c³ -3abc=(a+b+b)(a²+b²+c²-ab-bc-ca)

do a+b+c=0=> a³ + b³ + c³ = 3abc

Answer 2

hình như đề bài là Cho a+b+c=0.CM: a³+b³+c³=3abc

Answer 3

ta có:a+b+c=0 =>a+b=-c

                   <=>(a+b)³=-c³

                   <=>a³+b³+3ab(a+b)=-c³

                   <=>a³+b³+3ab(-c)=-c³  (vì a+b=-c)

                   <=>a³+b³-3abc=-c³

                    <=>a³+b³+c³=3abc.(đpcm)