2023 AMC 10B Problems/Problem 22

Revision as of 13:54, 15 November 2023 by Technodoggo (talk | contribs) (Solution)

Solution

First, we get the trivial solution by ignoring the floor. $(x-2)(x-1) = 0$, we get $(2,1)$ as solutions.

Next, we see that $\lfloor{x}\rfloor^2-3x=0.$ This implies that $-3x$ must be an integer. We can guess and check $x$ as $\dfrac{k}{3}$ which yields $(\dfrac{2}{3},\dfrac{11}{3}).$