If Rolle's theorem holds for the function `f(x) = x^(3) + bx^(2) + ax + 5` on [1, 3] with `c = (2 + (1)/(sqrt3))`, find the value of a and b

Explanation

To solve the problem, we need to find the values of \( a \) and \( b \) for the function \( f(x) = x^3 + bx^2 + ax + 5 \) such that Rolle's theorem holds on the interval \([1, 3]\) with \( c = 2 + \frac{1}{\sqrt{3}} \).

### Step 1: Apply the conditions of Rolle's Theorem

Rolle's theorem states that if a function is continuous on a closed interval \([a, b]\) and differentiable on the open interval \((a, b)\), and if \( f(a) = f(b) \), then there exists at least one \( c \) in \((a, b)\) such that \( f'(c) = 0 \).

Here, we have:
- \( a = 1 \)
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