If `x ne 0 and x=2`, find `x^(2) + (1)/(x^(2))`

Answer

To solve the problem, we need to find the value of \( x^2 + \frac{1}{x^2} \) given that \( x = 2 \) and \( x \neq 0 \).

### Step-by-Step Solution:

1. **Substitute the value of \( x \)**:
Since we know \( x = 2 \), we can substitute this value into the expression \( x^2 + \frac{1}{x^2} \).

\[ x^2 + \frac{1}{x^2} = 2^2 + \frac{1}{2^2} \]

2. **Calculate \( x^2 \)**:
Now, calculate \( 2^2 \):

\[ 2^2 = 4 \]

3. **Calculate \( \frac{1}{x^2} \)**:
Next, calculate \( \frac{1}{2^2} \):

\[ \frac{1}{2^2} = \frac{1}{4} \]

4. **Combine the results**:
Now, we can combine the results from steps 2 and 3:

\[ x^2 + \frac{1}{x^2} = 4 + \frac{1}{4} \]

5. **Find a common denominator**:
To add \( 4 \) and \( \frac{1}{4} \), we need a common denominator. The common denominator here is \( 4 \):

\[ 4 = \frac{4 \times 4}{4} = \frac{16}{4} \]

6. **Add the fractions**:
Now, add \( \frac{16}{4} + \frac{1}{4} \):

\[ \frac{16}{4} + \frac{1}{4} = \frac{16 + 1}{4} = \frac{17}{4} \]

Thus, the final answer is:

\[ x^2 + \frac{1}{x^2} = \frac{17}{4} \]