Suppose `a,b,c` are in AP and `a^(2),b^(2),c^(2)` are in GP, If `agtbgtc` and `a+b+c=(3)/(2)`, than find the values of a and c.

Explanation

To solve the problem step by step, we will use the information given about the arithmetic progression (AP) and geometric progression (GP) of the numbers \(a\), \(b\), and \(c\).

### Step 1: Understanding the conditions
We know that \(a\), \(b\), and \(c\) are in AP. This means:
\[ 2b = a + c \]
We are also given that \(a + b + c = \frac{3}{2}\).
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