Understanding Solve output

Question

In Solve output for such as:

Solve[r^2 - 6 r - 3 s^2 + 8 s Sqrt[r] == 0 && 0 < s < 1, r, Reals]

Where in the documentation do I learn how to read the output?

score 0 · Answer 1 · answered Apr 05 '18 at 13:00

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without testing the code generally Solve gives you an answer in the form of list with i entries like {r-> x1, r-> x2} depending in your case how many i Real answers there are...based on your condition...If you write ?Solve you’ll get a snippet of the documentation for that command...and the >>will take you directly to the documentation itself.

answered Apr 05 '18 at 13:00

DrMrstheMonarch

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In particular, how do I read the result: – Leon David Roper Apr 05 '18 at 13:05
Root[9 s^4 - 28 s^2 #1 + (36 - 6 s^2) #1^2 - 12 #1^3 + #1^4 &, 2], 0 < s < 1] – Leon David Roper Apr 05 '18 at 13:05
@LeonDavidRoper See e.g. How do I work with Root objects? – Artes Apr 05 '18 at 13:47

score 0 · Answer 2 · answered Apr 05 '18 at 13:33

Region[ImplicitRegion[
  r^2 - 6 r - 3 s^2 + 8 s Sqrt[r] == 0 && 0 < s < 1, {r, s}], 
 FrameLabel -> {"r", "s"}, Frame -> True, AspectRatio -> 1]

Note I am using <=

RegionPlot[
 r^2 - 6 r - 3 s^2 + 8 s Sqrt[r] <= 0 && 0 < s < 1, {s, 0.001, 
  0.999}, {r, 0, 7}, FrameLabel -> Automatic]

 val=Table[Join @@ {{s}, 
        Flatten@Values@
          NSolve[r^2 - 6 r - 3 s^2 + 8 s Sqrt[r] == 0 && 0 < s < 1, r, 
           Reals]}, {s, 1/100, 1, 1/100}] // Most

score 0 · Answer 3 · answered Apr 05 '18 at 13:57

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To get an insight of the solution variety you can use

ContourPlot[r^2 - 6 r - 3 s^2 + 8 s Sqrt[r] == 0, {s, 0, 1}, {r, -1, 6}, 
MaxRecursion -> 4, FrameLabel -> {s, r}]

The plot includes the solution s=r=0

answered Apr 05 '18 at 13:57

Ulrich Neumann

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Understanding Solve output

3 Answers3