Consider three distinct real numbers a,b,c in a G.P with `a^2+b^2+c^2=t^2` and a+b+c =`alpha t` .The sum of the common ratio and its reciprocal is denoted by S.
Complete set of `alpha^2` is

Options

A. 1,6,19
B. `sqrt(2).sqrt(50),sqrt(98)`
C. log 2,log 16 , log128
D. `sqrt(2),sqrt(3),sqrt(7)`

Explanation

To solve the problem, we need to analyze the given conditions and derive the complete set of \( \alpha^2 \).

### Step 1: Understanding the G.P. Condition
Let \( a, b, c \) be three distinct real numbers in a geometric progression (G.P.). We can express them in terms of a common ratio \( r \):
- \( b = ar \)
- \( c = ar^2 \)