If x, y, z are all distinct and |(x,x^(2...

If x, y, z are all distinct and `|(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 ` then value of x y z is :

A

`-1`

B

`-2`

C

1

D

2

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

If x,y,z are different and Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|=0 , show that xyz=-1

Prove the following identities : |{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x) .

If x != y != z and |[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]]|=0 then using properties of determinants, show that xyz= -1.

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

Show that |(1,x^2,x^3),(1,y^2,y^3),(1,z^2,z^3)| = (x-y),(y-z)(z-x)(xy+yz+zx)

For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - sqrt(2pi t) + 3pi The value of x + y + z is equal to

Prove that: {:|(1,x,x^3),(1,y,y^3),(1,z,z^3)| = (x-y)(y-z)(z-x)(x+y+z)