First off, x=0 is a trivial solution. There cannot be negative solutions.
If we ignore the [.] function we get x^3/24 = x^2 which has solution x=24. This is also a solution since each of x/2, x/3, x4 will not be rounded down.
The LHS of the equation is bounded above by x^3/24 and below by (x-2)(x-3)(x-4)/24. These cross the x^2 at x=24 and x=32.216 respectively.
A quick table shows no other solutions in this range. So the solution set is {0,24}
There is an additional non-integer solution at sqrt(882)=29.7 where the equation becomes 14*9*7=882
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Posted by Jer
on 2020-10-14 08:54:30 |
Solution
