If `alpha, beta and gamma` the roots of the equation `x^(3) + 3x^(2) - 4x - 2 = 0.`
then find the values of the following expressions:
(i) `alpha ^(2) + beta^(2) + gamma^(2)`
(ii)`alpha ^(3) + beta^(3) + gamma^(3)`
(iii) `(1)/(alpha)+(1)/(beta)+(1)/(gamma)`

Explanation

To solve the problem, we will use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. The given polynomial is:

\[ x^3 + 3x^2 - 4x - 2 = 0 \]

Let the roots of the polynomial be \( \alpha, \beta, \gamma \).

### Step 1: Find the sums and products of the roots

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