If `alpha,beta ` be the roots of the equation `3x^2+2x+1=0,` then find value of `((1-alpha)/(1+alpha))^3+((1-beta)/(1+beta))^3`

Explanation

To solve the problem, we need to find the value of \(\left(\frac{1 - \alpha}{1 + \alpha}\right)^3 + \left(\frac{1 - \beta}{1 + \beta}\right)^3\), where \(\alpha\) and \(\beta\) are the roots of the equation \(3x^2 + 2x + 1 = 0\).

### Step 1: Find the roots of the equation
The roots of the quadratic equation \(ax^2 + bx + c = 0\) can be found using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
For our equation \(3x^2 + 2x + 1 = 0\), we have \(a = 3\), \(b = 2\), and \(c = 1\).
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