Question

If $x,y,z\in R$ & $\Delta =\left|\begin{array}{ccc}x& x+y& x+y+z\\ 2x& 5x+2y& 7x+5y+2z\\ 3x& 7x+3y& 9x+7y+3z\end{array}\right|=-16$ then value of $x$ is

• A. $-2$
• B. $-3$
• C. $2$
• D. $3$

Answer 1

Answer: (A)

$-2$

Given,

$\left|\begin{array}{ccc}x& x+y& x+y+z\\ 2x& 5x+2y& 7x+5y+2z\\ 3x& 7x+3y& 9x+7y+3z\end{array}\right|=-16$

[ $R_2^{\prime }=R_2-2\times R_1$ and $R_3^{\prime }=R_3-3\times R_1$]

or, $\left|\begin{array}{ccc}x& x+y& x+y+z\\ 0& 3x& 5x+3y\\ 0& 4x& 6x+4y\end{array}\right|=-16$

or, $x\{18x^2+12xy-20x^2-12xy\}=-16$

or, $-2x^3=-16$

or, $x^3=8$

or, $x=2$.