If a2 + b2 + c2 - ab - bc - ca = 0 then a : b : c is?

Answer: Option D

$$\begin{array}{rl}& \text{Given, }\\ & a^2+b^2+c^2-ab-bc-ca=0\\ & \text{Find, }a:b:c=?\\ & \text{According to the question, }\\ & a^2+b^2+c^2-ab-bc-ca=0\\ & \Rightarrow a^2+b^2+c^2=ab+bc+ca\\ & \text{Let }a=b=c=1\\ & \Rightarrow 1^2+1^2+1^2=1\times 1+\left(1\times 1\right)+\left(1\times 1\right)\\ & \Rightarrow 3=3\\ & \Rightarrow \text{So, ratio of }a:b:c=1:1:1\end{array}$$