Let $S$ be the set of rational numbers $x$ such that $x^3-432$ is the square of a rational number.

If $S$ is infinite, enter $-1$. If $S$ is finite, enter the sum of the elements of $S.$

**Here is a very helpful hint:**

If $y^2=x^3-432,$ let
$u = \dfrac{36-y}{6x}, \, v = \dfrac{36+y}{6x}$. What is $u^3+v^3$?

×

Problem Loading...

Note Loading...

Set Loading...