If `a ,b ,c` are three distinct real numbers in G.P. and `a+b+c=x b ,` then prove that either x < -1 or x > 3

Explanation

To prove that either \( x < -1 \) or \( x > 3 \) given that \( a, b, c \) are three distinct real numbers in G.P. and \( a + b + c = x b \), we will follow these steps:

### Step 1: Represent the terms in G.P.
Let \( a, b, c \) be in G.P. Then we can express them as:
- \( b = ar \)
- \( c = ar^2 \)

where \( a \) is the first term and \( r \) is the common ratio.
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