Dao Trong Luan:Not right

\(-3\left(a-b\right)\left(b-c\right)\left(a-b+b-c\right)\)

\(=-3\left(a-b\right)\left(b-c\right)\left(a-c\right)=3\left(a-b\right)\left(b-c\right)\left(c-a\right)\)

(a−b)3+(b−c)3+(c−a)3=(a−b+b−c)3−3(a−b)(b−c)(a−b+b−c)+(c−a)3

=(a−c)3−3(a−b)(b−c)(c−a)−(a−c)3=−3(a−b)(b−c)(c−a)

⇒−3(a−b)(b−c)(c−a)=210

⇒(a−b)(b−c)(c−a)=−70

⇒|a−b|⋅|b−c|⋅|c−a|=70=2⋅5⋅7

But a,b,c are integer => |a−b|+|b−c|+|c−a|=2+5+7=14

Dao Trong Luan : not right

I agree with Alone

\(\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3=\left(a-b+b-c\right)^3-3\left(a-b\right)\left(b-c\right)\left(a-b+b-c\right)+\left(c-a\right)^3\)

\(=\left(a-c\right)^3-3\left(a-b\right)\left(b-c\right)\left(c-a\right)-\left(a-c\right)^3=-3\left(a-b\right)\left(b-c\right)\left(c-a\right)\)

\(\Rightarrow-3\left(a-b\right)\left(b-c\right)\left(c-a\right)=210\)

\(\Rightarrow\left(a-b\right)\left(b-c\right)\left(c-a\right)=-70\)

\(\Rightarrow\left|a-b\right|\cdot\left|b-c\right|\cdot\left|c-a\right|=70=2\cdot5\cdot7\)

But a,b,c are integer => \(\left|a-b\right|+\left|b-c\right|+\left|c-a\right|=2+5+7=14\)

I'm sorry .Let a,b,c............