During a calculation for a physics lab, I ran into the following six non-linear equations with unknowns $x_1,x_2,x_3,x_4,x_5,x_6 \in \mathbb{R}$
Solve[{(1 + x1*0.405^2/((0.405)^2 - x2) +
x3*0.405^2/((0.405)^2 - x4) + x5*0.405^2/((0.405)^2 - x6) ==
2.337053326), (1 + x1*(0.635)^2/((0.635)^2 - x2) +
x3*(0.635)^2/((0.635)^2 - x4) + x5*(0.635)^2/((0.635)^2 - x6) ==
2.293038467), (1 + x1*(0.670)^2/((0.670)^2 - x2) +
x3*(0.670)^2/((0.670)^2 - x4) + x5*(0.670)^2/((0.670)^2 - x6) ==
2.289560279), (1 + x1*(0.780)^2/((0.780)^2 - x2) +
x3*(0.780)^2/((0.780)^2 - x4) + x5*(0.780)^2/((0.780)^2 - x6) ==
2.277436534), (1 + x1*(0.808)^2/((0.808)^2 - x2) +
x3*(0.808)^2/((0.808)^2 - x4) + x5*(0.808)^2/((0.808)^2 - x6) ==
2.275719732), (1 + x1*(0.850)^2/((0.850)^2 - x2) +
x3*(0.850)^2/((0.850)^2 - x4) + x5*(0.850)^2/((0.850)^2 - x6) ==
2.272264106), (1 + x1*(0.880)^2/((0.880)^2 - x2) +
x3*(0.880)^2/((0.880)^2 - x4) + x5*(0.880)^2/((0.880)^2 - x6) ==
2.268823405), (1 + x1*(0.980)^2/((0.980)^2 - x2) +
x3*(0.980)^2/((0.980)^2 - x4) + x5*(0.980)^2/((0.980)^2 - x6) ==
2.265389225)}, {x1, x2, x3, x4, x5, x6}]
This code does not yield any output by Mathematica, and I cannot figure out wether I'm using the wrong command or wrong syntax or something else...
Assuming that Mathematica knows methods to solving this, how do I tell the program to do so and return the values of my $x_1,\ldots,x_6$ ?
Any help is very much appreciated. ;)
EDIT: By deleting the last two equations and writing it as
Solve[
1 + x1*0.405^2/((0.405)^2 - x2) + x3*0.405^2/((0.405)^2 - x4) +
x5*0.405^2/((0.405)^2 - x6) == 2.337053326
&&
1 + x1*(0.635)^2/((0.635)^2 - x2) + x3*(0.635)^2/((0.635)^2 - x4) +
x5*(0.635)^2/((0.635)^2 - x6) == 2.293038467
&&
1 + x1*(0.670)^2/((0.670)^2 - x2) + x3*(0.670)^2/((0.670)^2 - x4) +
x5*(0.670)^2/((0.670)^2 - x6) == 2.289560279
&&
1 + x1*(0.780)^2/((0.780)^2 - x2) + x3*(0.780)^2/((0.780)^2 - x4) +
x5*(0.780)^2/((0.780)^2 - x6) == 2.277436534
&&
1 + x1*(0.808)^2/((0.808)^2 - x2) + x3*(0.808)^2/((0.808)^2 - x4) +
x5*(0.808)^2/((0.808)^2 - x6) == 2.275719732
&&
1 + x1*(0.850)^2/((0.850)^2 - x2) + x3*(0.850)^2/((0.850)^2 - x4) +
x5*(0.850)^2/((0.850)^2 - x6) == 2.272264106
, {x1, x2, x3, x4, x5, x6}
]
the computer returns a result, but one that I do not understand. The following output was generated by Mathematica:
{{x1 -> 1.27242, x2 -> 0.00816205, x3 -> -0.000117262, x4 -> 0.563865,
x5 -> 0.0192823, x6 -> 1.70608},
{x1 -> 1.27242, x2 -> 0.00816205,
x3 -> 0.0192823, x4 -> 1.70608, x5 -> -0.000117262,
x6 -> 0.563865},
{x1 -> -0.000117262, x2 -> 0.563865, x3 -> 1.27242,
x4 -> 0.00816205, x5 -> 0.0192823,
x6 -> 1.70608},
{x1 -> -0.000117262, x2 -> 0.563865,
x3 -> 0.0192823, x4 -> 1.70608, x5 -> 1.27242,
x6 -> 0.00816205},
{x1 -> 0.0192823, x2 -> 1.70608, x3 -> 1.27242,
x4 -> 0.00816205, x5 -> -0.000117262,
x6 -> 0.563865},
{x1 -> 0.0192823, x2 -> 1.70608,
x3 -> -0.000117262, x4 -> 0.563865, x5 -> 1.27242,
x6 -> 0.00816205}}
Shouldn't this just be one value for each of the variables, instead of six each???
Reduce
returnsfalse
, which suggests that the equations are inconsistent. $\endgroup$