Question

cho a + b + c = 0. chứng minh rằng \(a^3+b^3+c^3\)=3abc

Answer 1

Ta có : a + b + c = 0

\(\Rightarrow\)a + b = - c

\(\Rightarrow\left(a+b\right)^3=\left(-c\right)^3\\ \Rightarrow a^3+3a^2b+3ab^2+b^3=-c^3\\ \Rightarrow a^3+b^3+c^3=-3ab\left(a+b\right)\\ \Rightarrow a^3+b^3+c^3=-3ab.\left(-c\right)\\ \Rightarrow a^3+b^3+c^3=3ab\left(đpcm\right)\)

Answer 2

ta có:a+b=(-c)

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

a^2+3a^2b+3ab^2+b^3=(-c)^3

a^3+b^3+c^3= -3a^2b+3ab^2

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

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

a^3+b^3+c^3=3abc