] gives the values of parameters that make the equations eqns valid for all values of the variables vars.
Equations are given in the form lhs
Simultaneous equations can be combined either in a list or with &&.
A single variable or a list of variables can be specified.
Example: SolveAlways[a x + b == 0, x].
SolveAlways works primarily with linear and polynomial equations.
SolveAlways produces relations between parameters that appear in eqns, but are not in the list of variables vars.
] is equivalent to Solve[!Eliminate[!
See the Mathematica book: Section 3.4.10.
See also: Eliminate, Solve, Reduce, PolynomialReduce.
Here is a simple example.
This fails because it involves transcendentals.
SolveAlways::ifun: Inverse functions are being used by SolveAlways, so some solutions may not be found.
This is how to make it work.
We check the result.