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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
1 month, 3 weeks ago

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Understand if you can Prince Loomba · 1 month, 2 weeks ago

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Only 1 solution is possible

\(a=\sqrt{30}/3\)

\(b=\sqrt{30}/4\)

\(c=2\sqrt{30}/5\)

For positive a,b,c Prince Loomba · 1 month, 3 weeks ago

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@Prince Loomba I think there are multiple solutions. I just tried it out with Desmos Hung Woei Neoh · 1 month, 3 weeks ago

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@Hung Woei Neoh Are they all positive real numbers? Prince Loomba · 1 month, 3 weeks ago

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@Prince Loomba You can have negative numbers Hung Woei Neoh · 1 month, 3 weeks ago

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@Hung Woei Neoh I gave only positive Prince Loomba · 1 month, 3 weeks ago

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@Prince Loomba can you please illustrate how did you find that solution.? Raghav Rathi · 1 month, 2 weeks ago

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Divide equations and then set up an inequality for the floor function? Not to sure though. Ian Limarta · 1 month, 3 weeks ago

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