If the roots of the equation `1/ (x+p) + 1/ (x+q) = 1/r` are equal in magnitude but opposite in sign, show that `p+q = 2r` & that the product of roots is equal to `(-1/2)(p^2+q^2)`.

Explanation

To solve the problem, we start with the equation given:

\[ \frac{1}{x+p} + \frac{1}{x+q} = \frac{1}{r} \]

### Step 1: Clear the fractions
Multiply both sides by \((x+p)(x+q)r\) to eliminate the denominators:
...