Question

Solve: $\left[\begin{array}{ccc}5& 10& 8\\ 3& 2& 6\\ 8& x+9& 9\end{array}\right]=100$.

Answer 1

$\left[\begin{array}{ccc}5& 10& 8\\ 3& 2& 6\\ 8& x+9& 9\end{array}\right]$=$100$

$\Rightarrow 5(18-6x-54)-3(90-8x-72)+8(60-16)=100$ (by the property of determinant, opening the determinant)

$\Rightarrow 90-30x-270-270+24x+216+480-128=100$

$\Rightarrow 118-6x=100$

$\Rightarrow 6x=18$

$\Rightarrow x=3$