If `ax=by=cz` ,prove that: `x^2/(yz)+y^2/(zx)+z^2/(xy)=(bc)/a^2+(ca)/b^2+(ab)/c^2`

If x+y+2z=0 then prove that x^2/(yz)+y^2/(zx)+(8z^2)/(xy)=6

If x + y + z = 0 , then the value of (x^2)/(yz) + (y^2)/(zx) + (z^2)/(xy) is:

If x/a = y/b = z/c , then show that (x^(2)-yz)/(a^(2)-bc) = (y^(2)-zx)/(b^(2) - ca) = (z^(2)-xy)/(c^(2)-ab)

Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)

Prove that |(x,x^2,yz),(y,y^2,zx),(z,z^2,xy)|= (x-y)(y-z)(z-x)(xy + yz + zx) .

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

If x : a = y : b = z : c , then prove that (a^(2) + b^(2) + c^(2))(x^(2) + y^(2) + z^(2)) = (ax + by + cz)^(2)

If x^2/(by+cz)=y^2/(cz+ax)=z^2/(ax+by)=1 then show that a/(a+x)+b/(b+y)+c/(c+z)=1

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