Find the valuesof `m` for which exactly one root of the equation `x^(2)-2mx+m^(2)-1=0` lies in the interval `(-2,4)`

Explanation

To solve the problem of finding the values of \( m \) for which exactly one root of the equation \( x^2 - 2mx + m^2 - 1 = 0 \) lies in the interval \( (-2, 4) \), we can follow these steps:

### Step 1: Identify the equation and its discriminant
The given quadratic equation is:
\[ x^2 - 2mx + (m^2 - 1) = 0 \]
To determine the nature of the roots, we calculate the discriminant \( D \):
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