Question

If $x^4+y^4+z^4=0$, then $\left|\begin{array}{ccc}1& xy& yz\\ zx& 1& xy\\ yz& zx& 1\end{array}\right|=$ ___________ (where x, y, z $\in$ R)

• A. $1$
• B. $x+y+z+3$
• C. $xyz+2$
• D. $0$

Answer 1

The correct option is A $1$

$x^4+y^4+z^4=0$

Since, $x,y,z\in R$

$\therefore x=y=z=0$

$\left|\begin{array}{ccc}1& xy& yz\\ zx& 1& xy\\ yz& zx& 1\end{array}\right|$

$=\left|\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right|$

$=1$

The answer is option (A).