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1)

For any three positive real numbers a,b and c. If 9(25a2+b2)+25(c2-3ac)  =15b (3a+c), then


A) b,c and a are in GP

B) b,c and a are in AP

C) a,b and c are in AP

D) a, b and c are in GP

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[(15a3b)2+(3b5c)2+(5c15a)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