If 2x&5 8&x = 6&-2 7&3 , then x = - Vidyadip

MCQ

If $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix},$ then $x =$

A
$3$
B
$\pm3$
✓
$\pm6$
D
$6$

✓

Answer

Correct option: C.

$\pm6$

$\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix}$
$\Rightarrow2\text{x}^2-40=18+14$
$\Rightarrow2\text{x}^2-40=32$
$\Rightarrow2\text{x}^2=72$
$\Rightarrow\text{x}^2=36$
$\Rightarrow\text{x}=\pm6$
Hence, the correct option is $(C)$

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