For any three positive real numbers `a , b` and `c ,9(25 a^2+b^2)+25(c^2-3a c)=15 b(3a+c)dot` Then : (1)`a ,b` and`c` are in`AdotP` (2) `a ,b` and `c` are in `GdotP` (3)`b ,c` and `a` are in `GdotP` (4) `b , c` and `a` are in `AdotP`

Options

A. a,b and c are in GP
B. b,c and a are in GP
C. b,c and a are in AP
D. a,b and c are in AP

Explanation

To solve the given equation and determine the relationship between the numbers \( a, b, \) and \( c \), we start with the equation:

\[ 9(25a^2 + b^2) + 25(c^2 - 3ac) = 15b(3a + c) \]

### Step 1: Expand and Rearrange the Equation

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