[R] Solving two nonlinear equations with two knowns

[yhsu6 at illinois.edu]

Dear R users, 

I have two nonlinear equations, f1(x1,x2)=0 and f2(x1,x2)=0. I try to use optim command by minimize f1^2+f2^2 to find x1 and x2. I found the optimal solution changes when I change initial values. How to solve this? 

BTW, I also try to use grid searching. But I have no information on ranges of x1 and x2, respectively. 

Any suggestion to solve this question? 

Thanks, 

Kate