If the equation `x^(4)-4x^(3)+ax^(2)+bx+1=0` has four positive roots, find the values of a and b.

Explanation

To solve the equation \(x^4 - 4x^3 + ax^2 + bx + 1 = 0\) with the condition that it has four positive roots, we can follow these steps:

### Step 1: Understand the properties of the roots
Let the roots of the polynomial be \(x_1, x_2, x_3, x_4\). According to Vieta's formulas:
- The sum of the roots \(x_1 + x_2 + x_3 + x_4 = 4\) (coefficient of \(x^3\) with a negative sign).
- The product of the roots \(x_1 x_2 x_3 x_4 = 1\) (constant term).

### Step 2: Apply the Arithmetic Mean-Geometric Mean Inequality (AM-GM)
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