n equations n+1 unknowns (one known unknown!) in Matlab
Would like to solve a problem. I think it's equivalent to n simultaneous equations with n+1 unknowns.
There won't be an explicit solution but what I'd like to do is express the solutions in terms of the extra unknown. It's a known unknown :-) It's actually the simultaneous equations from a lagrange multiplier problem.
I can do this by hand, no problem. Any ideas on what to use in Matlab please? (I did verify the 'theme' by putting k = 1,2,3 ... in Matlab but how to have it remain as k....)
Here's a concrete example so you see what I mean ...
y^2*k - 2*h*x = 0
2*k*x*y^(2*k-1) - 2*h*y = 0
x^2 = 1 - y^2
I'd like to express the solutions for x, y, h in terms of k.
By hand I get (+/- 1/sqrt(2k+1), +/- sqrt(2k)/sqrt(2k+1)) for (x,y), which is all I'm interested in really.
Thanks for your help!