Solve symbolic cubic equation and select specific solution

Questions
,
1

Hello,

I try to solve some equations and automatically select the right solution when assuming certain parameter properties.

Test.png
Test.png812Ă—142 2.7 KB

How can I automatically select the right of those three solutions when assuming the result must always be a Real number and that the parameters a & b are both Reals and both are bigger than 0.

Thanks a lot for your help,

Bernd
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Test.png&userId=1869958

Test.nb (2.65 KB)

2

Hi Bernd,

Try

Solve[a*t^3 == b && a > 0 && b > 0, t, Reals]
3

Rohit’s solution gives a Root object, which may not be desirable.

To do the selection after the fact, use

    In[1]:= soln = Solve[a t^3 == b, t]
    
    Out[1]= {{t -> b^(1/3)/a^(
       1/3)}, {t -> -(((-1)^(1/3) b^(1/3))/a^(1/3))}, {t -> ((-1)^(2/3)
         b^(1/3))/a^(1/3)}}
    
    In[2]:= Select[soln, 
       Simplify[Element[(t /. #), Reals], Assumptions -> {a > 0, b > 0}] &]

    Out[2]= {{t -> b^(1/3)/a^(1/3)}}
4

Another option

Solve[a*t^3 == b && a > 0 && b > 0, t, Reals] // ToRadicals // Normal

(* {{t -> ((-1)^(2/3) b^(1/3))/a^(1/3)}} *)