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

Let Delta_(1)=|{:(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1):}| and Delta_(2)=|{:(A,B,C),(x,y,z),(yz,zx,xy):}| , then :

Prove the following : |(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=0 .

If x + y + z = 0 , then the value of (x^2)/(yz) + (y^2)/(zx) + (z^2)/(xy) is:

if x=31,y=32 and z=33 then the value of |{:((x^(2)+1)^(2),,(xy+1)^(2),,(xz+1)^(2)),((xy+1)^(2),,(y^(2)+1)^(2),,(yz+1)^(2)),((xz+1)^(2),,(yz+1)^(2),,(z^(2)+1)^(2)):}|" is " "____"

If x,y,z are distinct and |(x, x(x^2+1), x+1),(y,y(y^2+1), y+1),(z, z(z^2+1), z+1)|=0 then (A) xyz=0 (B) x+y+z=0 (C) xy+yz+zx=0 (D) x^2+y^2+z^2=1

Using the properties of determinants, show that: abs((x,x^2,yz),(y,y^2,xz),(z,z^2,xy))=(x−y)(y−z)(z−x)(xy+yz+zx)

Show that Delta =Delta_(1) , where Delta = |[Ax,x^(2), 1],[By, y^(2), 1],[Cz, z^(2),1]| "and "Delta_(1) = |[A,B, C],[x, y, z],[zy, zx,xy]|

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zy,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(y-z)(z-x)(x-y)(yz+zy+xy)