If `a^2+b^2+c^2-ab-bc-ca=0`, prove that `a=b=c`

Explanation

Given:

`=> a^2+b^2+c^2-a b-b c-c a=0`

To prove `a=b=c`

Multiplying with both side by `2`. we get.

`=> 2(a^2+b^2+c^2-a b-b c-c a=0)`

`=> 2a^2+2b^2+2c^2-2a b-2b c-2c a=0`

`=> (a^2+b^2-2a b)+(b^2+c^2-2b c)+(c^2+a^2-2c a)`

`=> (a-b)^2+(b-c)^2+(c-a)^2`

...