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

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

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

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

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

If x,y and z are three different numbers, then 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