I'm trying to solve the following system of equations for ahat0, ahat1, ahat2 using the Solve function.

I know (algebraically) that a system exists, but Mathematica isn't converging. I've triple checked my syntax, and I'm unsure what's going on (i.e. why Mathematica won't give me a solution). Attaching the equations and the code here to explain what I mean.

Solve[{ahat0 + ahat1 t + ahat2 t^2 - m bar == 0,
  ahat0 t + ahat1 t^2 + ahat2 t^3 - mtbar == 0,
  ahat0 t^2 + ahat1 t^3 + ahat2 t^4 - mt2bar == 0},
  {ahat0, ahat1, ahat2}]

enter image description here

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    $\begingroup$ In a new fresh notebook and replacing Solve with Reduce returns an answer in a fraction of a second. Then Simplify that result to make it even smaller. $\endgroup$ – Bill Oct 15 '18 at 22:40
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    $\begingroup$ What does the bar over t, t^2 etc. mean? It probably means that $\overline{t^2}$ does not equal $\overline{t}^2$ $\endgroup$ – Carl Woll Oct 15 '18 at 23:55
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    $\begingroup$ Based on the way you wrote all the other variable names in your little block of code, and thank you profusely for including that block of code, that is so helpful, you might have wanted mbar as a single variable with no space between m and bar rather than m bar with a space in the middle which makes that into two variables multiplied together. If there is that space or not then Solve returns {} indicating that it could find no solution. Reduce on the other hand finds one kind of solution with the space present and a different solution with the space removed. Hopefully this helps $\endgroup$ – Bill Oct 16 '18 at 3:02
  • $\begingroup$ @Bill - Oddly, adding the option Method -> Reduce to Solve does not return a result even though the documentation for Solve states "With Method -> Reduce, Solve uses Reduce to find the complete solution set" $\endgroup$ – Bob Hanlon Oct 16 '18 at 4:47
  • $\begingroup$ @CarlWoll the bar over (t_bar)^2 means an average (t_bar) was squared, (t^2)bar means that t was squared, then the average was taken. you are correct that the two terms are not equal. $\endgroup$ – wiscoYogi Oct 16 '18 at 5:04

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