If `alpha,beta,gamma` are the roots of the equation `x^3 + 4x +1=0` then `(alpha+beta)^(-1)+(beta+gamma)^(-1)+(gamma+alpha)^(-1)=`

Explanation

To solve the problem, we need to find the value of \((\alpha + \beta)^{-1} + (\beta + \gamma)^{-1} + (\gamma + \alpha)^{-1}\) given that \(\alpha, \beta, \gamma\) are the roots of the polynomial \(x^3 + 4x + 1 = 0\).

### Step-by-Step Solution

1. **Identify the Coefficients**:
The polynomial is given as \(x^3 + 0x^2 + 4x + 1 = 0\). Here, we can identify:
- \(a = 1\) (coefficient of \(x^3\))
- \(b = 0\) (coefficient of \(x^2\))
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