Show that the solution in Example 3.13 converges quadratically.

Data from Example 3.13

Solve the system of Eqs. (3.7.6) and (3.7.7) using Newton’s method with an initial guess x⁽⁰⁾₁ = 0 and x⁽⁰⁾₂ = 0.

fi(x, x) = ex1 - x f2(x, x) = x + x - 3x2 (3.7.6) (3.7.7)