List of top Applied Mathematics Questions on Determinants

Using properties of determinants, prove that
\[ \Delta = \begin{vmatrix} (b + c)^2 & a^2 & a^2 \\ b^2 & (c + a)^2 & b^2 \\ c^2 & c^2 & (a + b)^2 \end{vmatrix} = 2abc(a + b + c)^3 \]

If \( \left| \begin{array}{cc} 2x & 5 \\ 4 & x \end{array} \right| = \left| \begin{array}{cc} 3 & 5 \\ 4 & 6 \end{array} \right| \), then the value of \( x \) is: