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Input:

Reduce[3  x^2 - 2 a x + a^2 - 1 >= 0 && x > a, x] // TraditionalForm

Output:

(a<=-Sqrt[(3/2)]\[And]x>a)
\[Or](-Sqrt[(3/2)]<a<-(1/Sqrt[2])\[And](a<x<=a/3-1/3 Sqrt[3-2 a^2]\[Or]x>=1/3 Sqrt[3-2 a^2]+a/3))
\[Or](-(1/Sqrt[2])<=a<1/Sqrt[2]\[And]x>=1/3 Sqrt[3-2 a^2]+a/3)\[Or](a>=1/Sqrt[2]\[And]x>a)

My Solution by hand:

My Solution by hand:

  • This has already been asked and closed as a duplicate; see: (13905) – Mr.Wizard Jul 29 '13 at 14:48
  • @ m_goldberg，Is it possible to get the step by step process of Reduce? –  Jul 29 '13 at 15:29
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    I don't think it is a duplicate. Nonetheless I doubt there can be a general remedy to this problem, even though WolframAlpha can offer some half-measures. On the other hand certain restricted problems can be easily resolved. – Artes Jul 29 '13 at 19:44
  • @ Artes,Can I think that Person's solution is different from Mathematica's solution? –  Jul 30 '13 at 05:12
  • @tangshutao If you ask anyone you should call him @name (without space between @ and name). I'm not sure what you mean. The problem with your question is that you haven't asked it precisely. Of course you can do much with e.g. Reduce, but it is difficult to decide what is needed especially and what can be omitted. In WolframAlpha there is the Show Steps option, but I'm not sure about its scope. You could perform some experiments and then it will be more likely that your question could find some constructive answers. – Artes Jul 30 '13 at 13:55

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