If `(x^(3)+y^(3) )prop (x^(3)-y^(3)) `, then prove that (x+y) `prop` (x-y).

If (x^6+(1)/(y^6)) prop (x^6-(1)/(y^6)) , then prove that y prop 1/x .

If (x+y) prop (x-y), then prove that (x^(2)+y^(2)) prop xy .

if (px^3+qy^3) prop (ax^3+by^3) ,then show that x prop y

If (x+y) prop (x-y) , then prove that (ax +by) prop (px+qy) where a ,b ,p, q are non -zero variation constant.

If (x+y) prop (x-y) , then show that (x^(3) +y^(3)) prop (x^(3)-y^(3)) .

If (3x-4y) prop sqrt(xy) then show that (x^2+y^2) prop xy .

If ((1)/(x)-(1)/(y))prop1/(x-y) ,then show that (x^2 + y^2)propxy .

If (1)/(y^n)+(1)/(z^n)prop (1)/(Y^n+z^n) then prove that y prop z .

If (x^3+y^3) alpha(x^3-y^3) prove that (x^2+y^2) alpha(x^2-y^2) .