If n is a root of `x^(2)(1-ac)-x(a^(2)+c^(2))-(1+ac)=0` and if n harmonic means are inserted between a and c, find the difference between the first and the last means.

Explanation

To solve the problem, we need to find the difference between the first and last harmonic means inserted between two numbers \( a \) and \( c \), given that \( n \) is a root of the equation:

\[ x^2(1 - ac) - x(a^2 + c^2) - (1 + ac) = 0 \]

### Step 1: Identify the quadratic equation
The given equation can be rewritten as:
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