If `a^(2) + (1)/(a^(2)) = 18 and a ne 0`, find:
`a- (1)/(a)`

Answer

To solve the problem where \( a^2 + \frac{1}{a^2} = 18 \) and we need to find \( a - \frac{1}{a} \), we can follow these steps:

### Step 1: Use the identity for \( a - \frac{1}{a} \)
We know that:
\[ \left( a - \frac{1}{a} \right)^2 = a^2 - 2 + \frac{1}{a^2} \]
This can be rearranged to:
\[ \left( a - \frac{1}{a} \right)^2 = a^2 + \frac{1}{a^2} - 2 \]

### Step 2: Substitute the given value
We are given that:
\[ a^2 + \frac{1}{a^2} = 18 \]
Substituting this into the identity gives:
\[ \left( a - \frac{1}{a} \right)^2 = 18 - 2 \]

### Step 3: Simplify the equation
Now, simplifying the right side:
\[ \left( a - \frac{1}{a} \right)^2 = 16 \]

### Step 4: Take the square root
Taking the square root of both sides, we have:
\[ a - \frac{1}{a} = \pm 4 \]

### Conclusion
Thus, the values of \( a - \frac{1}{a} \) are:
\[ a - \frac{1}{a} = 4 \quad \text{or} \quad a - \frac{1}{a} = -4 \]