find real numbers

nickolas

Find real numbers $x,$ such that $x^2-\lfloor x\rfloor^2=1$

**Posted:** Wed Nov 04, 2009 6:58 am

Tomekk

Hello,

I assume I did a mistake here, but I cannot find it Blush

.

We need to prove $x^{2} - \lfloor x\rfloor^{2} = 1$

And after that : $\lfloor x\rfloor^{2} = x^{2} - 1$

Since $\lfloor x\rfloor^{2}$ is an integer, so must $x^{2} - 1$ be an integer.

And from there $x^{2}$ must be an integer, so we can write:

$x^{2} = x^{2} - 1$ . So no solutions. Blush

**Posted:** Wed Nov 04, 2009 8:03 am

JBL

$\lfloor x \rfloor ^2 \neq \lfloor x^2 \rfloor$ .

For example, $\sqrt{2}$ is certainly a solution of the original equation.

**Posted:** Wed Nov 04, 2009 8:49 am

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Joel
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Yongyi781

Your mistake

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**Posted:** Thu Nov 05, 2009 4:27 am

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