Let `alphaa n dbeta` be the solutions of the quadratic equation `x^2-1154 x+1=0` , then the value of `alpha^(1/4)+beta^(1/4)` is equal to ______.

Explanation

To solve the problem, we need to find the value of \( \alpha^{1/4} + \beta^{1/4} \) given that \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 - 1154x + 1 = 0 \).

### Step 1: Identify the roots of the quadratic equation
The roots \( \alpha \) and \( \beta \) can be found using Vieta's formulas, which state:
- \( \alpha + \beta = 1154 \)
- \( \alpha \beta = 1 \)

### Step 2: Calculate \( \alpha^{1/2} + \beta^{1/2} \)
We can find \( \alpha^{1/2} + \beta^{1/2} \) using the identity:
\[ (\alpha^{1/2} + \beta^{1/2})^2 = \alpha + \beta + 2\sqrt{\alpha \beta} \]
Substituting the values we have:
\[ (\alpha^{1/2} + \beta^{1/2})^2 = 1154 + 2\sqrt{1} \]
\[ (\alpha^{1/2} + \beta^{1/2})^2 = 1154 + 2 = 1156 \]
Taking the square root of both sides:
\[ \alpha^{1/2} + \beta^{1/2} = \sqrt{1156} = 34 \]

### Step 3: Calculate \( \alpha^{1/4} + \beta^{1/4} \)
Next, we need to find \( \alpha^{1/4} + \beta^{1/4} \). We can use the identity:
\[ (\alpha^{1/4} + \beta^{1/4})^2 = \alpha^{1/2} + \beta^{1/2} + 2\sqrt{\alpha^{1/2} \beta^{1/2}} \]
Since \( \alpha^{1/2} \beta^{1/2} = \sqrt{\alpha \beta} = \sqrt{1} = 1 \):
\[ (\alpha^{1/4} + \beta^{1/4})^2 = 34 + 2\sqrt{1} \]
\[ (\alpha^{1/4} + \beta^{1/4})^2 = 34 + 2 = 36 \]
Taking the square root of both sides:
\[ \alpha^{1/4} + \beta^{1/4} = \sqrt{36} = 6 \]

### Final Answer
Thus, the value of \( \alpha^{1/4} + \beta^{1/4} \) is \( \boxed{6} \).