Let `alpha` and `beta` be roots of the equation `X^(2)-2x+A=0` and let `gamma` and `delta` be the roots of the equation `X^(2)-18x+B=0`. If `alpha lt beta lt gamma lt delta` are in arithmetic progression then find the valus of A and B.

Explanation

To solve the problem, we need to find the values of \( A \) and \( B \) given the roots of two quadratic equations and the condition that the roots are in arithmetic progression.

### Step 1: Identify the roots of the first equation
The first equation is given as:
\[ x^2 - 2x + A = 0 \]
Let the roots be \( \alpha \) and \( \beta \). By Vieta's formulas:
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