Answer:
Option C
Explanation:
We have,
225a2+9b2+25c2-75ac-45ab-15bc=0
⇒(15a)2+(3b)2+(5c)2−(15a)(5c)−(15a)(3b)−(3b)(5c)=0
⇒12[(15a−3b)2+(3b−5c)2+(5c−15a)2]=0
⇒15a=3b,3b=5c and 5c=15a
∴ 15a=3b=5c
\Rightarrow \frac{a}{1}=\frac{b}{5}=\frac{c}{3}=\lambda(say)
\Rightarrow a=\lambda,b=5\lambda ,c=3\lambda
Hence, a,b and c are in A.P