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Iterated Floor Illation (Posted on 2022-10-28) Difficulty: 3 of 5
Determine all possible real numbers x that satisfy this equation:
           4x⌊3x⌊x⌋⌋ = 2022
Note: ⌊n⌋ denotes floor(n), that is, the greatest integer less than or equal to n.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution computer-assisted solution | Comment 1 of 22
fplot(@(x)4*x*floor(3*x*floor(x))-2022)
grid on

creates a graph which can be zoomed in to find a zero at x ~= 5.810344828.

This is close enough to find

>> floor(3*x*floor(x))
ans =
    87
>> f=ans*4
f =
   348
>> f=sym(348)
f =
348
>> sym(2022)/f
ans =
337/58
>> eval(ans)
ans =
          5.81034482758621
          
so the answer is 337/58 ~= 5.81034482758621.          

  Posted by Charlie on 2022-10-28 11:52:28
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