If x, y and z are all different and |x&x2&1+x3 y&y2&1+y3 z&z2&1+z3|=0 then

Question

If x, y and z are all different and |x&x2&1+x3 y&y2&1+y3 z&z2&1+z3|=0 then (A)  xyz = -1  (B)  xyz = 1  (C)  xyz = -2  (D)  xyz = 2

Tardigrade Admin · Accepted Answer

Given , | beginmatrixx&x2&1+x3 y&y2&1+y3 z&z2&1+z3 endmatrix|=0 ⇒ | beginmatrixx&x2&1 y&y2&1 z&z2&1 endmatrix|+| beginmatrixx&x2&x3 y&y2&y3 z&z2&z3 endmatrix|=0 ⇒ | beginmatrixx&x2&1 y&y2&1 z&z2&1 endmatrix|+xyz | beginmatrix1&x&x2 1&y&y2 1&z&z2 endmatrix|=0 ⇒ | beginmatrixx&x2&1 y&y2&1 z&z2&1 endmatrix|+xyz| beginmatrixx&x2&1 y&y2&1 z&z2&1 endmatrix|=0 ⇒ (1+xyz) | beginmatrixx&x2&1 y&y2&1 z&z2&1 endmatrix|=0 ⇒ (1+xyz)| beginmatrixx&x2&1 y&y2&1 z&z2&1 endmatrix|=0 ⇒ 1+xyz=0 and | beginmatrixx&x2&1 y&y2&1 z&z2&1 endmatrix|≠0 ∴ xyz=-1

Q. If $x, y$ and $z$ are all different and
$∣ ∣ x y z x^{2} y^{2} z^{2} 1 + x^{3} 1 + y^{3} 1 + z^{3} ∣ ∣ = 0$ then

$x yz = - 1$

$x yz = 1$

$x yz = - 2$

$x yz = 2$

Q. If x,y and z are all different and ∣∣​xyz​x2y2z2​1+x31+y31+z3​∣∣​=0 then

xyz=−1

xyz=1

xyz=−2

xyz=2

Q. If $x, y$ and $z$ are all different and
$∣ ∣ x y z x^{2} y^{2} z^{2} 1 + x^{3} 1 + y^{3} 1 + z^{3} ∣ ∣ = 0$ then

$x yz = - 1$

$x yz = 1$

$x yz = - 2$

$x yz = 2$