if ` (a^(2) +2bc) ,( b^(2) +2ac) ,(c^(2) +2ab) ` are in AP, show that
`1 / (( b-c)) ,1/((c -a)) , 1/ ((a-b)) are in AP.

Explanation

To show that \( \frac{1}{b-c}, \frac{1}{c-a}, \frac{1}{a-b} \) are in AP given that \( (a^2 + 2bc), (b^2 + 2ac), (c^2 + 2ab) \) are in AP, we will follow these steps:

### Step 1: Understand the condition for AP
We know that three terms \( x, y, z \) are in AP if \( 2y = x + z \).

### Step 2: Apply the condition for the given terms
Given that \( (a^2 + 2bc), (b^2 + 2ac), (c^2 + 2ab) \) are in AP, we can write:
\[
...