Giải:
a2(b - c) + b2(c - a) + c2(a - b) = 0
\(\Rightarrow\) a2(b - c) + b2c - ab2 + ac2 - bc2 = 0
\(\Rightarrow\) a2(b - c) + bc(b - c) - a(b2 - c2) = 0
\(\Rightarrow\) a2(b - c) + bc(b - c) - a(b - c)(b + c) = 0
\(\Rightarrow\) (b - c)(a2 + bc - ab - ac) = 0
\(\Rightarrow\) (b - c)[a(a - b) - c(a - b)] = 0
\(\Rightarrow\) (a - b)(a - c)(b - c) = 0
\(\Rightarrow\) \(\left[{}\begin{matrix}a-b=0\\a-c=0\\b-c=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}a=b\\a=c\\b=c\end{matrix}\right.\)
\(a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)=0\)
\(a^2b-a^2c+b^2c-ab^2+c^2a-c^2b=0\)
\(\left(a-b\right)\left(b-c\right)\left(c-a\right)=0\)
=>\(a-b=0hoacb-c=0hoacc-a=0\)
=>\(a=b\) hoặc b=c hoặc c=a
=>a=b=c(đpcm)
\(a^2(b−c)+b^2(c−a)+c^2(a−b)=0 a^2b−a^2c+b^2c−ab^2+c^2a−c^2b=0\)
(a−b)(b−c)(c−a)=0
=>a−b=0hoacb−c=0hoacc−a=0
=>a=bhoặc b=c hoặc c=a(đpcm)
