If $$a^2 + 13b^2 + c^2 - 4ab - 6bc = 0$$, then a:b:c is

Expression : $$a^2 + 13b^2 + c^2 - 4ab - 6bc = 0$$

=> $$a^2+4b^2-2(a)(2b)+9b^2+c^2-2(3b)(c)=0$$

=> $$(a-2b)^2+(3b-c)^2=0$$

Since, sum of two positive numbers is zero, thus both the numbers = 0

=> $$a-2b=0$$ and $$3b-c=0$$

=> $$a=2b$$ and $$3b=c$$

Multiplying by '3', we get :

=> $$3a=6b$$ and $$9b=3c$$

=> $$\frac{a}{b}=\frac{6}{3}$$ and $$\frac{b}{c}=\frac{3}{9}$$

=> $$a:b:c=6:3:9$$

=> Required ratio = $$2:1:3$$

=> Ans - (C)