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I'm new to Mathematica. I usually used Wolfram Alpha; however, since the equation that I'm working with is a long equation I need to use Mathematica. This is an example of the problem. So, I want to know if the equation will have solution or not when m >= 4 and n >= 3.41421 m. I don't know what command to use and when I enter this, it said that m >= 4 is not a valid variable`. What should I do?

Solve[{Binomial[n - 1, 2] - 2[(Binomial[m - 1, 2]) + (n - m)(m - 1) - 1] <= 0}, {m >= 4, n >= 3.41421 m}, Reals]
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This can be done by the command

FindInstance[ Binomial[n - 1, 2] -  2 ((Binomial[m - 1, 2]) + (n - m) (m - 1) - 1) <= 0 &&
 m >= 4 && n >= 3.41421*m, {m, n}, Reals]
   (*{{m -> 537343., n -> 1.8346*10^6}}*)
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  • $\begingroup$ Thank you so much for answering my question. It works. $\endgroup$
    – Iras
    Feb 8 at 22:22

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