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 \( a^2 + \frac{1}{a^2} = 7 \) and \( a \neq 0 \).

### Step-by-step Solution:

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

2. **Use the identity for \( (a - \frac{1}{a})^2 \)**:
The identity states:
\[ (a - \frac{1}{a})^2 = a^2 - 2 + \frac{1}{a^2} \]
Rearranging gives us:
\[ (a - \frac{1}{a})^2 = a^2 + \frac{1}{a^2} - 2 \]

3. **Substitute the known value**:
Substitute \( a^2 + \frac{1}{a^2} = 7 \) into the equation:
\[ (a - \frac{1}{a})^2 = 7 - 2 \]
Simplifying this gives:
\[ (a - \frac{1}{a})^2 = 5 \]

4. **Take the square root of both sides**:
To find \( a - \frac{1}{a} \), take the square root:
\[ a - \frac{1}{a} = \pm \sqrt{5} \]

5. **Final answer**:
Therefore, the solution is:
\[ a - \frac{1}{a} = \sqrt{5} \text{ or } -\sqrt{5} \]