Question

Solve equation $\left|\begin{array}{ccc}5& 6& 1\\ 6& 4& 5\\ 2& 3& -9\end{array}\right|+\left|\begin{array}{ccc}x& 4& 6\\ 2& 3& -9\\ 5& 6& -1\end{array}\right|$ $=\left|\begin{array}{ccc}2& 3& -9\\ 2x-1& -8& -11\\ 5& 6& 1\end{array}\right|$

Answer 1

$\left|\begin{array}{ccc}5& 6& 1\\ 6& 4& 5\\ 2& 3& -9\end{array}\right|$ $+$ $\left|\begin{array}{ccc}x& 4& 6\\ 2& 3& -9\\ 5& 6& -1\end{array}\right|$ $=$ $\left|\begin{array}{ccc}2& 3& -9\\ 2x-1& -8& -11\\ 5& 6& 1\end{array}\right|$

$⟹\left\{5\right(-36-15)-6(-54-10)+1(18-8\left)\right\}+\left\{x\right(-3+54)-4(-2+45)+6(12-15\left)\right\}=2(-8+66)-3(2x-1+55)-9(12x-6+40)$

$⟹-255+384+10+51x-172-18=116-6x-162-108x-306$

$⟹165x=-301$

$⟹x=1.82$