An equation that hp prime can't solve

[roadrunner]

fsolve works best if you give it a starting point. If:

PHP Code:

(f(λ,μ)) := (λ^4+λ^3*μ^2+λ^2*μ^2+λ^2*μ+λ^2+λ*μ^4+λ*μ^2+3*λ*μ*sqrt(λ^4+4*λ^3*μ+4*λ^3+2*λ^2*μ^2+4*λ^2*μ+2*λ^2+4*λ*μ^3+4*λ*μ^2+4*λ*μ+4*λ+μ^4+4*μ^3+2*μ^2+4*μ+1)+μ^3+μ)/(λ^3*μ+λ*μ^3+λ*μ);

dfx := (simplify(∂(f(x,y),x)));

dfy := (simplify(∂(f(x,y),y))); 


then fsolve({dfx = 0,dfy = 0},{x,y},{1.1,1.1}) returns {1.,1.}.

I gave up waiting for solve([dfx=0,dfy=0],[x,y]) to return an answer.

-road