Why mathematica does not solve the equation $x\left \lfloor x \right \rfloor=10$ for $x$?

Question

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?

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]. — user64494, Jul 10, 2020 at 9:31

Emmet · Accepted Answer · 2020-07-10 06:22:03Z

7

You can specify you want real solutions

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

answered Jul 10, 2020 at 6:22

Emmet

3561 silver badge6 bronze badges

$\begingroup$ 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, 2020 at 9:28
1

$\begingroup$ 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, 2020 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, 2020 at 20:08

Add a comment |

1 Answer 1