Math Gold Medalist

Lor

2023 AMC 12A 

Problem 23

How many ordered pairs of positive real numbers $(a,b)$ satisfy the equation\[(1+2a)(2+2b)(2a+b) = 32ab?\]

$\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }\text{an infinite number}$

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   Solution