`x^(2)+y^(2)+2(xy-yz-zx)`

Factorise : x^(2)+y^(2)+z^(2)-xy-yz-zx

If x,y and z are three different numbers, then prove that : x^(2) + y^(2) + z^(2)- xy - yz- zx is always positive

Express ((x^(3)+y^(3)+z^(3)-3xyz)/((x^(2)+y^(2)+z^(2)-xy-yz-zx))) in lowest terms

If x^(2) + y^(2) + z^(2) - xy- yz - zx = 0 , prove that : x= y = z

If x=997 , y=998 z=999 then the value of x^(2)+y^(2)+z^(2)-xy-yz-zx will be

Prove that x^(2)+y^(2)+z^(2)-xy-yz-zx is always positive.

If ax+cy+bz=X, cx+by+az=Y, bx+ay+cz=Z, show that (a^(2)+b^(2)+c^(2)-bc-ca-ab)(x^(2)+y^(2)+z^(2)-yz-zx-xy)=X^(2)+Y^(2)+Z^(2)-YZ-ZX-XY

If (x^(2)+y^(2)+z^(2)-64)/(xy-yz-zx)=-2 and x+y=3z, then the value of z is (a) 2 (b) 3 (c) 4 (d) None of these

If x=a+b,y=b+c,z=c+a , prove that (x+y+z)xx{x^(2)+y^(2)+z^(2)-xy-yz-zx}=2(a^(3)+b^(3)+c^(3)-3abc)