Question

If \[\begin{vmatrix}2x & 5 \\ 8 & x\end{vmatrix} = \begin{vmatrix}6 & - 2 \\ 7 & 3\end{vmatrix}\] , write the value of x.

Answer 1

\[\begin{vmatrix}2x & 5 \\ 8 & x\end{vmatrix} = \begin{vmatrix}6 & - 2 \\ 7 & 3\end{vmatrix}\] 
\[ \Rightarrow 2 x^2 - 40 = 18 + 14\] 
\[ \Rightarrow 2 x^2 - 40 = 32\] 
\[ \Rightarrow 2 x^2 = 72\] 
\[ \Rightarrow x^2 = 36\] 
\[ \Rightarrow x = \pm 6\] 
Hence, the value of x is \pm 6 .