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If x,y,z are different and Delta= {:|(x,...

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

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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 then show that 1+xyz=0

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)

Knowledge Check

  • 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
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    B
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    C
    1
    D
    2

    • Similar Questions

    Explore conceptually related problems

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

    Prove that abs{:(x, x^2 , 1 + px^3),(y , y^2, 1+ py^3),(z, z^2, 1+ pz^3):}= (1 +pxyz) ( x-y) ( y-z) ( z-x) , where p is any scalar.

    Prove that abs{:(x, x^2 , 1 + px^3),(y , y^2, 1+ py^3),(z, z^2, 1+ pz^3):}= (1 +pxyz) ( x-y) ( y-z) ( z-x) , where p is any scalar.

    Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(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.

    If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0 , then prove that : xyz(xy+yz+zx)=x+y+z

    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) .

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