If `|{:(x,2),(8,x):}|=|{:(3,2),(9,6):}|`, then the value of 'x' is ...........

Answer

To solve the equation \( | \begin{pmatrix} x & 2 \\ 8 & x \end{pmatrix} | = | \begin{pmatrix} 3 & 2 \\ 9 & 6 \end{pmatrix} | \), we will calculate the determinants of both matrices and set them equal to each other.

### Step-by-Step Solution:

1. **Calculate the determinant of the left matrix**:
\[ | \begin{pmatrix} x & 2 \\ 8 & x \end{pmatrix} | = x \cdot x - 8 \cdot 2 = x^2 - 16 \]

2. **Calculate the determinant of the right matrix**:
\[ | \begin{pmatrix} 3 & 2 \\ 9 & 6 \end{pmatrix} | = 3 \cdot 6 - 9 \cdot 2 = 18 - 18 = 0 \]

3. **Set the determinants equal to each other**:
\[ x^2 - 16 = 0 \]

4. **Solve the equation**:
\[ x^2 = 16 \]
Taking the square root of both sides, we get:
\[ x = \pm 4 \]

5. **Conclusion**:
The values of \( x \) that satisfy the equation are \( x = 4 \) and \( x = -4 \).