This problem is from Numerical Analysis. I can solve this in general but given the numerical solution, should I solve for a numerical answer by hand? I'm having some trouble with understanding the application.

3. Consider the polynomial system of equations 9-x2 6-1)? : -1 16-)? + l4-x : 33 and we consider (x0, yo) : (0.667, 1.249) as a numerical solution. (i) Formulate a constrained optimization problem to determine the backward error (ii) Set up the equations for solving the constrained optimization problems using the Lagrange multipliers. (iii) Extra credit: Formulate the backward error problem as a minimumnorm solution of a linear equation