If ` a^(2) +b^(2) = 13` and ab= 6 find:
` a+b`

Answer

To solve the problem, we need to find the value of \( a + b \) given that \( a^2 + b^2 = 13 \) and \( ab = 6 \).

### Step-by-step Solution:

1. **Use the identity for \( (a + b)^2 \)**:
\[ (a + b)^2 = a^2 + b^2 + 2ab \]

2. **Substitute the known values**:
We know \( a^2 + b^2 = 13 \) and \( ab = 6 \). Substitute these values into the identity:
\[ (a + b)^2 = 13 + 2 \cdot 6 \]

3. **Calculate \( 2ab \)**:
\[ 2 \cdot 6 = 12 \]

4. **Add the values together**:
\[ (a + b)^2 = 13 + 12 = 25 \]

5. **Take the square root**:
To find \( a + b \), take the square root of both sides:
\[ a + b = \sqrt{25} \]

6. **Simplify the square root**:
\[ a + b = 5 \quad \text{or} \quad a + b = -5 \]

### Final Answer:
Thus, the values of \( a + b \) are \( 5 \) or \( -5 \).