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If \(\begin{vmatrix}2x & 5\\8 & x\end{vmatrix}=\begin{vmatrix}6 & -2\\7 & 3\end{vmatrix}\), then the value of x is |
-6 only 6 only -6 or 6 3 |
-6 or 6 |
The correct answer is Option 3: -6 or 6 To solve for $x$, we need to evaluate the determinants on both sides of the given equation. For a $2 \times 2$ determinant, the value is calculated as: $\begin{vmatrix} a & b \\ c & d \end{vmatrix} = (a \times d) - (b \times c)$
Given equation: $\begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix} = \begin{vmatrix} 6 & -2 \\ 7 & 3 \end{vmatrix}$ $\text{LHS} = (2x \cdot x) - (5 \cdot 8)$
$\text{LHS} = 2x^2 - 40$
$\text{RHS} = (6 \cdot 3) - (-2 \cdot 7)$
$\text{RHS} = 18 - (-14)$
$\text{RHS} = 18 + 14 = 32$
Equate LHS and RHS to solve for $x$$2x^2 - 40 = 32$
$2x^2 = 72$
$x^2 = 36$
$x = 6 \text{ or } -6$
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