If `|{:(x,12),(3,x):}|=|{:(6,18),(2,6):}|`, then value of 'x' is

Options

A. `+-4`
B. `+-6`
C. `+-8`
D. None of these

Answer

To solve the equation \( |(x, 12), (3, x)| = |(6, 18), (2, 6)| \), we will first compute the determinants on both sides and then equate them.

### Step 1: Calculate the determinant on the left side
The left side determinant is given by:
\[ |(x, 12), (3, x)| = x \cdot x - 12 \cdot 3 = x^2 - 36 \]

### Step 2: Calculate the determinant on the right side
The right side determinant is given by:
\[ |(6, 18), (2, 6)| = 6 \cdot 6 - 18 \cdot 2 = 36 - 36 = 0 \]

### Step 3: Set the two determinants equal to each other
Now, we set the two determinants equal:
\[ x^2 - 36 = 0 \]

### Step 4: Solve for \( x \)
To solve for \( x \), we can rearrange the equation:
\[ x^2 = 36 \]
Taking the square root of both sides gives us:
\[ x = \pm 6 \]

### Final Answer
Thus, the values of \( x \) are \( 6 \) and \( -6 \).

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