Question

CM: \(a^3+b^3+c^3=3abc\) thì a+b+c=0 hoặc a=b=c

Answer 1

bạn ơi có thiếu +3 hay j ko

Answer 2

Answer 3

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

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

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

\(=> [(a+b)^3+c^3] - 3ab(a+b+c) = 0\)

\(=> (a+b+c)[(a+b)^2-c(a+b)+c^2]-3ab(a+b+c)=0\)

\(=> (a+b+c)(a^2+b^2+c^2+2ab-bc-ca)-3ab(a+b+c)=0\)

\(=> (a+b+c)(a^2+b^2+c^2+2ab-bc-ca-3ab)=0\)

\(=> (a+b+c)(a^2+b^2+c^2-ab-bc-ca)=0\)

\(\Rightarrow\left[{}\begin{matrix}a+b+c=0\\a^2+b^2+c^2-ab-bc-ca=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}a+b+c=0\\a=b=c\end{matrix}\right.\)