Question

a+b+c=0.CM :a³+b³+c³=3abc

Answer 1

\(a^3+b^3+c^3-3abc=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ac\right)\)

Do \(a+b+c=0\)

\(\Rightarrow a^3+b^3+c^3-3abc=0\Rightarrow a^3+b^3+c^3=3abc\)

Answer 2

a+b+c=0\(\Rightarrow\)a+b= -c

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

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

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