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# [Help Me!] Simulataneous Floor Equations

$\lfloor a \rfloor bc = 3 \\ a \lfloor b \rfloor c = 4 \\ ab \lfloor c \rfloor = 5$

If $$a,b$$ and $$c$$ are real numbers satisfying the system of equations above. Find all solutions of $$(a,b,c)$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

I wasn't able to find all the solutions, so i request the community to provide the total solutions.

Note by Raghav Rathi
4 months ago

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Understand if you can · 4 months ago

Only 1 solution is possible

$$a=\sqrt{30}/3$$

$$b=\sqrt{30}/4$$

$$c=2\sqrt{30}/5$$

For positive a,b,c · 4 months ago

I think there are multiple solutions. I just tried it out with Desmos · 4 months ago

Are they all positive real numbers? · 4 months ago

You can have negative numbers · 4 months ago

I gave only positive · 4 months ago

can you please illustrate how did you find that solution.? · 4 months ago