If the difference between the corresponding roots of the equations `x^(2)+ax+b=0` and `x^(2)+bx+a=0(a1=b)` is the same, find the value of `a+b`.

Explanation

To solve the problem, we need to find the value of \( a + b \) given that the difference between the corresponding roots of the equations \( x^2 + ax + b = 0 \) and \( x^2 + bx + a = 0 \) is the same.

### Step-by-Step Solution:

1. **Identify the Roots**:
Let the roots of the first equation \( x^2 + ax + b = 0 \) be \( \alpha \) and \( \beta \).
Let the roots of the second equation \( x^2 + bx + a = 0 \) be \( \gamma \) and \( \delta \).

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