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

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.

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TopNewestUnderstand 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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– Hung Woei Neoh · 1 month, 3 weeks ago

I think there are multiple solutions. I just tried it out with DesmosLog in to reply

– Prince Loomba · 1 month, 3 weeks ago

Are they all positive real numbers?Log in to reply

– Hung Woei Neoh · 1 month, 3 weeks ago

You can have negative numbersLog in to reply

– Prince Loomba · 1 month, 3 weeks ago

I gave only positiveLog in to reply

– Raghav Rathi · 1 month, 2 weeks ago

can you please illustrate how did you find that solution.?Log in to reply

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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