Question

Cho a+b+c=0. CMR: a³+b³+c³=3abc

Answer 1

a +b +c =  0 => a + b = - c

Ta có 

 a^3 + b^3 + c^3 = ( a + b)^3 - 3ab( a+b) + c^3

  Thay a+ b= -c ta có

a^3 + b^3 + c^3 = -c^3 - 3ab.-c + c^3 = 3abc

=> ĐPCM

Answer 2

Ta có : \(a^3+b^3+c^3-3abc=\left(a+b\right)^3-3a^2b-3ab^2+c^3-3abc=\left[\left(a+b\right)^3\right]-3ab\left(a+b+c\right)\)\(=\left(a+b+c\right)\left[\left(a+b\right)^2-\left(a+b\right)c+c^2\right]-3ab\left(a+b+c\right)=0\)

\(\Rightarrow a^3+b^3+c^3=3abc\)