Making mathematica solve a complicated system [closed]

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:

How can I make Mathematica solve this system?

• 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. Jan 16, 2017 at 13:18
• Otherwise use the option MaxExtraConditions -> All. The Mathematica will give you the conditions on the parameters under which there is a solution for a. Jan 16, 2017 at 13:19
• 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. Jan 16, 2017 at 13:20

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