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Difference between revisions of "2021 April MIMC 10 Problems/Problem 21"

(Created page with "How many solutions are there for the equation <math>\left \lfloor{x}\right \rfloor^{2}-\left \lceil{x}\right \rceil=0</math>. (Recall that <math>\left \lfloor{x}\right \rfloor...")
 
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<math>\textbf{(A)} ~0 \qquad\textbf{(B)} ~1 \qquad\textbf{(C)} ~2 \qquad\textbf{(D)} ~3 \qquad\textbf{(E)} ~4 \qquad</math>
 
<math>\textbf{(A)} ~0 \qquad\textbf{(B)} ~1 \qquad\textbf{(C)} ~2 \qquad\textbf{(D)} ~3 \qquad\textbf{(E)} ~4 \qquad</math>
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==Solution==
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To be Released on April 26th.

Revision as of 17:51, 22 April 2021

How many solutions are there for the equation $\left \lfloor{x}\right \rfloor^{2}-\left \lceil{x}\right \rceil=0$. (Recall that $\left \lfloor{x}\right \rfloor$ is the largest integer less than $x$, and $\left \lceil{x}\right \rceil$ is the smallest integer larger than $x$.)

$\textbf{(A)} ~0 \qquad\textbf{(B)} ~1 \qquad\textbf{(C)} ~2 \qquad\textbf{(D)} ~3 \qquad\textbf{(E)} ~4 \qquad$

Solution

To be Released on April 26th.

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