If `|(x,2),(18,x)| = |(6,2),(18,6)|`, then the value of x is:

Options

A. `overset""+-2`
B. `overset""+-4`
C. `overset""+-6`
D. `overset""+-8`

Answer

To solve the equation given by the determinants, we start by writing down the determinants explicitly:

1. **Write the Determinants:**
We have two determinants to equate:
\[ |(x, 2), (18, x)| = |(6, 2), (18, 6)| \]

2. **Calculate the Determinants:**
The determinant of a 2x2 matrix \(|(a, b), (c, d)|\) is calculated as \(ad - bc\).

For the left-hand side:
\[ |(x, 2), (18, x)| = x \cdot x - 2 \cdot 18 = x^2 - 36 \]

For the right-hand side:
\[ |(6, 2), (18, 6)| = 6 \cdot 6 - 2 \cdot 18 = 36 - 36 = 0 \]

3. **Set the Determinants Equal:**
Now we set the two determinants equal to each other:
\[ x^2 - 36 = 0 \]

4. **Solve for \(x\):**
Rearranging gives:
\[ x^2 = 36 \]
Taking the square root of both sides, we get:
\[ x = \pm 6 \]

5. **Final Answer:**
Therefore, the values of \(x\) are:
\[ x = 6 \quad \text{or} \quad x = -6 \]