Question

CMR: Với a+b+c=0 hoặc a=b=c thì a³+b³+c³=3abc.

Answer 1

Ta có: \(a=b=c\Rightarrow\hept{\begin{cases}a^3=abc\\a^3=b^3=c^3\end{cases}}\)

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

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

Answer 2

\(a+b+c=0\)

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

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

\(\Leftrightarrow a^3+3ab\left(a+b\right)+b^3+c^3=0\)

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

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