Then A (A+1)> 2013> A (A). If A> 44, the right side is not satisfied. If A <45, then the left side is not satisfied. No solutions in this case.

Case 2. X <0. (Again, let the floor of X be A)

Then \(A^{2}> 2013 >A(A+1)\).

Note that A=-45 is the only solution. This gives x=\(-\frac {2013}{45}\) as the only solution.
–
Joel Tan
·
2 years ago

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@Joel Tan
–
Well dude still I'didn't get 2013 as the asnwer even by using a calculator.
–
Jaiveer Shekhawat
·
2 years ago

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@Jaiveer Shekhawat
–
You might be mistaken. \(\lfloor -\frac{2013}{45} \rfloor = \lfloor -44.7333 \ldots \rfloor = -45\) instead of \(-44\) as you might have thought. You can then see that \(x \lfloor x \rfloor = 2013\) very easily.
–
Jake Lai
·
2 years ago

@Math Man
–
It is not complete, as the case for x <0 was not considered. There is one solution, as shown in my solution above.
–
Joel Tan
·
2 years ago

## Comments

Sort by:

TopNewestCase 1. X> 0. Let the floor of X be A.

Then A (A+1)> 2013> A (A). If A> 44, the right side is not satisfied. If A <45, then the left side is not satisfied. No solutions in this case.

Case 2. X <0. (Again, let the floor of X be A)

Then \(A^{2}> 2013 >A(A+1)\).

Note that A=-45 is the only solution. This gives x=\(-\frac {2013}{45}\) as the only solution. – Joel Tan · 2 years ago

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– Jaiveer Shekhawat · 2 years ago

Well dude still I'didn't get 2013 as the asnwer even by using a calculator.Log in to reply

– Jake Lai · 2 years ago

You might be mistaken. \(\lfloor -\frac{2013}{45} \rfloor = \lfloor -44.7333 \ldots \rfloor = -45\) instead of \(-44\) as you might have thought. You can then see that \(x \lfloor x \rfloor = 2013\) very easily.Log in to reply

– Jaiveer Shekhawat · 2 years ago

Thanks...got the right nerveLog in to reply

44

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– Math Man · 2 years ago

thank youLog in to reply

– Joel Tan · 2 years ago

It is not complete, as the case for x <0 was not considered. There is one solution, as shown in my solution above.Log in to reply

jessen wkwkwkw:D – Alfian Edgar · 2 years ago

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– Math Man · 2 years ago

lolLog in to reply