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Apply the Newton-Raphson method to find a system root: x ^ 2 + y ^ 2...

Apply the Newton-Raphson method to find a system root:

x ^ 2 + y ^ 2 = 10

x ^ 2 - y ^ 2 = 1

Use the initial approximation x0 = 1 and y0 = 1.

You want to trust the result in at least 3 significant figures.

Solutions must approximate x = 2.34521 and y = 2.12132

Explain your answer step by step. In addition, if Excel is used, it will be necessary to include the formulas used.

Preferably I would like the calculation to be by hand, to understand more deeply how this method is used.

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