$\"\"$

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The equation is $\"\"$ and initial approximation is $\"\"$ .

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Newtons approximation formula : $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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From the newtons method, $\"\"$ .

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Substitutte $\"\"$ in above expression.

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$\"\"$

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Substitutte $\"\"$ in above expression.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Substitutte $\"\"$ in above expression.

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$\"\"$ .

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Substitutte $\"\"$ in above expression.

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$\"\"$

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Third approximation to the root of the equation is $\"\"$ .

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$\"\"$

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Third approximation to the root of the equation is $\"\"$ .