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I have the following system: $$ d^2 = at^6 + bt^2 + c \\e^2 = a(t + 1)^6 + b(t + 1)^2 + c \\f^2 = a(t + 2)^6 + b(t + 2)^2 + c$$

I'm trying to solve for a, b, and c in terms of the other variables.

If I naively try to solve this system:

Solve[{d^2 == a*t^6 + b*t^2 + c, e^2 == a (t + 1)^6 + b (t + 1)^2 + c,
   f^2 == a (t + 2)^6 + b (t + 2)^2 + c}, a]

It just returns an empty list. The actual solution is pretty complicated, but it's nothing that Mathematica can't handle: enter image description here

How can I make Mathematica solve this system?

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    $\begingroup$ The empty list means that there is no solution. Your system is overdetermined: one variable and three equations. Mathematica's response is correct. If a, b and c are all variables (and not parameters), specify that. Then you have a different system. $\endgroup$
    – Szabolcs
    Jan 16, 2017 at 13:18
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    $\begingroup$ Otherwise use the option MaxExtraConditions -> All. The Mathematica will give you the conditions on the parameters under which there is a solution for a. $\endgroup$
    – Szabolcs
    Jan 16, 2017 at 13:19
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    $\begingroup$ Have you looked in the documentation? The second "basic example" shows you how to solve systems of equations. reference.wolfram.com/language/ref/Solve.html EDIT: This was a response to a now deleted comment about how to specify variables. $\endgroup$
    – Szabolcs
    Jan 16, 2017 at 13:20

1 Answer 1

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The correct code is:

sol = Solve[{d^2 == a*t^6 + b*t^2 + c, e^2 == a (t + 1)^6 + b (t + 1)^2 + c,
   f^2 == a (t + 2)^6 + b (t + 2)^2 + c}, {a, b, c}]

You have to solve it with respect to a,b,c, not only a.

Maybe you were interested only in a, in that case you can do something on the line of:

A1 = a/.sol
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