If \( \begin{vmatrix}5 & -4\\ 5 & 4\end{vmatrix}=\begin{vmatrix}8 & x^{2}\\ -x & -3\end{vmatrix} \) then the value of \( x \) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
Expanding the two determinants:
\( \text{Left side}=5\cdot 4-(-4)(5)=40 \)
\( \text{Right side}=8(-3)-x^{2}(-x)=x^{3}-24 \)
Equating them,
\( x^{3}-24=40 \)
\( x^{3}=64 \)
so \( x=4 \).