" The determinant "|[xp+y,x,y],[yp+z,y,z],[0,xp+y,yp+z]|=0

The determinant |[x p+y, x, y], [y p+z, y, z],[0,x p+y, y p+z]|=0 if (a) x y z are in AP (b) x y z are in GP (c) x y z are in HP (d) xy yz zx are in AP

det [[xp + y, x, yyp + z, y, z0, xp + y, yp + z]] = 0 if

The determinant |xp+yxyyp+zyz0xp+yyp+z|=0 if x,y,z

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,y,z)| , is

The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,y,z)| , is

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)