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Rootfinding for Nonlinear Equations: Newton's Method

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51. Solve the system:

x^2 + xy^3 = 9

3x^2y - y^3 = 4

using Newton's method for nonlinear system. Use each of the initial guesses:

(x_0, y_0) = (1.2, 2.5), (-2, 2.5), (-1.2, -2.5), (2, -2.5)

Observe which root to which the method converges, the number or iterates required, and the speed of convergence.

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