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.
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.
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Posted by Charlie
on 2022-10-28 11:52:28 |
computer-assisted solution
