Question

solve p^3-4xy+8y^2=0​

Answer 1

The given equation is p3−4xyp+8y2=0 and the requirement is to solve for x.

This equation contains 3 variables if p is a variable. In such a case we need 3 equations to solve for x .

If p is not a variable we have an equation with 2 variables. In such a case we need 2 equations to solve for x .

In any case, we can express x as an explicit function of p and y, as under:

x=p3+8y24py.

We can also express y as an explicit function of p and x , as under:

y=2px±4p2x2−8p3√8=px±px2−2p√4.