2023 AMC 10B Problems/Problem 22

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 $(\dfrac{2}{3},\dfrac{11}{3}).$

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2023 AMC 10B Problems/Problem 22

Solution