Solving a system of nonlinear equations with given data in R?

Question

I wonder how to solve a system of nonlinear equations with given data in R? A sample code is as follows and I would like the function to be flexible to be able to receive different kinds of datasets (X,Y,Z). Here "par" is the vector of unknowns.

require("BB")
#data:
xi <- c(8.046,11.033,3.330,-0.281,2.829,1.764,5.432,5.576,4.565,3.3912382)
yi <- c(17.289,33.976,13.252,-3.699,15.776,-1.250,14.261,11.082,15.703,13.424)
zi <- c(4.967,8.047,9.036,13.851,9.215,12.087,11.204,7.775,7.713,12.760)

#function:
mepar.iter <- function(par,X,Y,Z){
  
  F <- rep(NA,length(par))
  
  F[1] <- par[1]*sum(X^2)+par[2]^2*sum(X+Y)+(2/par[3])*sum(1/sqrt(Z))
  
  F[2] <- par[1]^3*sum(X+Z)+2*par[2]*sum(Y)+par[3]*sum(Z)
  
  F[3] <- par[1]^0.5*sum(Y)+(par[2]/2)*sum(X+Y+Z)-par[3]
  
  F}

par0 <- rep(0,3)
dfsane(par=par0,fn=mepar.iter(par,xi,yi,zi), control = list(trace = FALSE))

This is just a code example, where equations F[1], F[2], and F[3] should be equal to zero, but the above code does not work effectively. Any helps would be appreciated!