Question

If (a – b)² + (b – c)² + (c – a)² = 0, then __________.

Answer 1

Given:$(a-b{)}^2+(b-c{)}^2+(c-a{)}^2=0$
$\Rightarrow (a-b{)}^2=0$ and $(b-c{)}^2=0$ and $(c-a{)}^2=0$
$\Rightarrow a-b=0$ and $b-c=0$ and $c-a=0$
$\Rightarrow a=b$ and $b=c$ and $c=a$
$\Rightarrow a=b=c$
Hence, if (a – b)² + (b – c)² + (c – a)² = 0, then a = b = c.