सिध्द कीजिए कि `2x^(2) + 2y^(2)+2z^(2)-2xy-2yz-2zx=[(x-y)^(2)+(y-z)^(2)+(z-x)^(2)]`

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

Simplify: (x+y+2z)(x^(2)+y^(2)+4z^(2)-xy-2yz-2zx)

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

[[x,x^(2),yzy,y^(2),zxz,z^(2),xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

Prove that quad det ([yx-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]) is divisible by (x+y+z) and hence find the quotient.

yz-x^(2)quad zx-y^(2)quad xy-z^(2)| Prove that det[[yz-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]] is divisible by (x+y+z), and hence find the quotient.

x+y-z=5 and x^(2)+y^(2)+z^(2)=29, find xy-yz-zx

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

Find the product: (x+y+2z)(x^(2)+y^(2)+4z^(2)-xy-2yz-2zx)

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