1. (25 points) Computer Problem: Apply the Newton's method and the modified Newton's method (J(it) J(7o)) to the nonlinear equations, 2} - a + 2x2 = 0, 2:r1 + 2 6 = 0. %3D with initial guess (-5,-4). Examine the rates of convergence of the two meth- ods. (Attach the code). 1. (25 points) Computer Problem: Apply the Newton's method and the modified Newton's method (J(it) J(7o)) to the nonlinear equations, 2} - a + 2x2 = 0, 2:r1 + 2 6 = 0. %3D with initial guess (-5,-4). Examine the rates of convergence of the two meth- ods. (Attach the code)