Question

please tell me the answer , i beg you

Answer 1

Answer:

x = 0   or   x = -1

Step-by-step explanation:

$\sf{\implies\begin{vmatrix}1&x&2x\\1&3x&5x\\1&3&4\end{vmatrix}}= 0}\\\\\\ R_3 \rightarrow R_3 - R_1\:\:\: also\:\:\:R_2 \rightarrow R_2 - R_1\\\\\sf{\implies\begin{vmatrix}1&x&2x\\1-1&3x-x&5x-2x\\1-1&3-x&4-2x\end{vmatrix}}= 0}\\\\\\\sf{\implies\begin{vmatrix}1&x&2x\\0&2x&3x\\0&3-x&4-2x\end{vmatrix}}= 0}\\\\\\\sf{\implies 1[2x(4 - 2x) - 3x(3 - x)] = 0}\\\\\sf{\implies 8x - 4x^2 - 9x + 3x^2 = 0 }\\\\\implies \sf{-x^2 -x = 0}\\\\\implies \sf{-x(x + 1) = 0}\\\\\sf{\implies x = 0\:\:or \:\: x = -1 }$