Given: `a^(2) + (1)/(a^(2))= 7 and a ne 0`, find
`a + (1)/(a)`

Answer

To solve the problem, we need to find the value of \( a + \frac{1}{a} \) given that \( a^2 + \frac{1}{a^2} = 7 \).

### Step-by-step Solution:

1. **Start with the given equation:**
\[ a^2 + \frac{1}{a^2} = 7 \]

2. **Recall the identity for \( (a + \frac{1}{a})^2 \):**
\[ (a + \frac{1}{a})^2 = a^2 + 2 + \frac{1}{a^2} \]

3. **Rearranging the identity:**
From the identity, we can express \( a^2 + \frac{1}{a^2} \) in terms of \( (a + \frac{1}{a})^2 \):
\[ (a + \frac{1}{a})^2 = a^2 + \frac{1}{a^2} + 2 \]

4. **Substituting the given value:**
Substitute \( a^2 + \frac{1}{a^2} = 7 \) into the equation:
\[ (a + \frac{1}{a})^2 = 7 + 2 \]
\[ (a + \frac{1}{a})^2 = 9 \]

5. **Taking the square root:**
To find \( a + \frac{1}{a} \), take the square root of both sides:
\[ a + \frac{1}{a} = \pm \sqrt{9} \]
\[ a + \frac{1}{a} = \pm 3 \]

### Final Answer:
Thus, the values of \( a + \frac{1}{a} \) are:
\[ a + \frac{1}{a} = 3 \quad \text{or} \quad a + \frac{1}{a} = -3 \]