Question: Solve the following equations by the Newton-Raphson method: [begin{array}{r}2 x_{1}^{2}+x_{2}^{2}-10=0 x_{1}^{2}-x_{2}^{2}+x_{1} x_{2}-4=0end{array}] Start with an initial guess of (x_{1}=1) and (x_{2}=1).

Solve the following equations by the Newton-Raphson method:

\[\begin{array}{r}2 x_{1}^{2}+x_{2}^{2}-10=0 \\x_{1}^{2}-x_{2}^{2}+x_{1} x_{2}-4=0\end{array}\]

Start with an initial guess of \(x_{1}=1\) and \(x_{2}=1\).

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