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The equation $x\left \lfloor x \right \rfloor=10$ has a real solution, which is $x=\frac{10}{3}$.

But when I type

Solve[x*Floor[x] == 10, x]

a message comes: "Solve::nsmet: This system cannot be solved with the methods available to Solve."

Similarly with NSolve.

I am using version 12.1.0.0. Anything wrong I did?

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  • $\begingroup$ A more serious issue with Reduce[Floor[x]^2 - x*Floor[x] + 3 == 0, x, Reals] and Reduce[Floor[x]^2 - x*Floor[x] + 3 <= 0, x, Reals]. $\endgroup$ – user64494 Jul 10 at 9:31
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You can specify you want real solutions

Solve[x*Floor[x] == 10, x, Reals]

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  • $\begingroup$ Unfortunately,Solve[Floor[x]^2 - x*Floor[x] + 3 == 0, x, Reals] fails Solve::nsmet: This system cannot be solved with the methods available to Solve. as well as Reduce. However,NSolve[Floor[x]^2 - x*Floor[x] + 3 == 0 && x >= 0 && x <= 10, x, Reals] works. $\endgroup$ – user64494 Jul 10 at 9:28
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    $\begingroup$ So does Reduce[Floor[x]^2 - x*Floor[x] + 3 == 0 && x >= 0 && x <= 10, x, Reals], outputting x == 19/4 || x == 28/5 || x == 13/2 || x == 52/7 || x == 67/8 || x == 28/3. $\endgroup$ – user64494 Jul 10 at 9:42
  • $\begingroup$ @user64494 Solve[{Floor[x]^2 - x*Floor[x] + 3 == 0, 0 < x < 10}, x, Reals] evaluates all solutions in the given interval ! $\endgroup$ – Ulrich Neumann Jul 10 at 20:08

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