Math Gold Medalist

Lor

2023 AMC 12A 

Problem 10

Positive real numbers $x$ and $y$ satisfy $y^3 = x^2$ and $(y-x)^2 = 4y^2$. What is $x+y$?

$\textbf{(A)}\ 12 \qquad \textbf{(B)}\ 18 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 36 \qquad \textbf{(E)}\ 42$

Priority: The Most Limited Case

y-x=+-2y so x=3y or x=-y

.

   Solution