umyIx r 1+x|. Z are different and Aay y 1+ y =0, thenz z1+z0show that I + 2

If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=0 , then

If z=x+i y and w=(1-i z)//(z-i) and |w| = 1 , then show that z is purely real.

If cos^(-1) x + cos^(-1) y + cos ^(-1) z = pi and 0 lt x,y,z lt 1 show that x^(2) +y^(2) +z^(2) +2xyz = 1

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 x/(x+2y+z) = y/(y+2z+x) = z/(z+2x +y) and x+y+z !=0 , then show that each ratio is equal to 1/4 .

If |[x^3+1, x^2, x] , [y^3+1, y^2, y] , [z^3+1, z^2, z]|=0 and x, y, z are all different then prove that xyz=-1

Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]] , Where x,y,z are different. Show that if Delta=0 ,then 1+xyz=0