show tha `|[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|`=0

Using the properties of determinants, show that: [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

The value of |{:(x,x^2-yz,1),(y,y^2-zx,1),(z,z^2-xy,1):}| is

Using Cofactors of elements of third column, evaluate Delta=|[1 , x, yz],[1, y, zx],[1, z, xy]|

If x,y,z are dinstinct 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)

solve |[1,yz,yz(y+z)],[1,zx,zx(z+x)],[1,xy,xy(x+y)]|

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-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 then show that 1+xyz=0

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

If "Delta"=|(1,x,x^2),( 1,y, y^2),( 1,z, z^2)| , "Delta"_1=|(1, 1, 1),(yz, z x,x y), (x, y, z)| , then prove that "Delta"+"Delta"_1=0 .

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a. 1 b. 2 c. -1 d. 2