perplexus.info :: Just Math : Integral part and fractional part equation

Integral part and fractional part equation (Posted on 2025-03-10)

Find all positive numbers x such that

 1     1      1
--- - ---- = ----
[x]   [2x]   6{x}

where [x] represents the integer part of x and {x}=x-[x].

No Solution Yet Submitted by Danish Ahmed Khan

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re: solution

| Comment 3 of 4 |

(In reply to solution by Charlie)

[8/3] = 2

{8/3} = 2/3

Plugging 8/3 into the equation:

 1     1      1
--- - ---- = ----
[x]   [2x]   6{x}

 1     1      1
--- - ---- = ----
 2     5      4

Posted by Larry on 2025-03-10 13:45:41

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