Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How do I find the real valued solutions to $3x - x^3 = \sqrt{(x + 2)}$.


Here we see three intersections of the two graphs $f(x) = 3x - x^3$ and $g(x) = \sqrt{(x + 2)}$. I don't see how this is possible since the two complex solutions are "plotted" even though the axes are real-valued.

share|improve this question

1 Answer 1

up vote 2 down vote accepted

Look at the approximate forms of the solutions: you'll notice that the imaginary part of the two "complex" solutions is something like $10^{-17}$. I guess that it's numerical noise.

share|improve this answer
Then what are the extra two things they are plotting? Why are they on the plots? –  Arthur Collé Oct 27 '12 at 19:23
@A.M.C.: There are indeed three real roots. WolframAlpha is merely expressing them using complex numbers; as Andrea says, the imaginary parts cancel out in the end. Sometimes this is necessary: see casus irreducibilis. –  Rahul Oct 27 '12 at 20:19
If the approximation comes out that low, it's likely that the true value of the imaginary part is $0$. The reason you see $i$ sprinkled throughout the given roots is that the general formula for roots of cubics requires the use of imaginary numbers, even when all roots are real. Presumably a full simplification would reveal an imaginary part of $0$ for all of the roots. –  Tabes Bridges Oct 27 '12 at 20:20

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.