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A numerical solution of the equation f(x) = x + √x − 3 = 0 can be obtained using Newton-Raphson method. If the starting value is x = 2 for the iteration, the value of x that is to be used in the next step is

1. 0.306
2. 0.739
3. 1.694
4. 2.306

Correct answer: 1.694

Solution

The Newton-Raphson method uses the formula xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) to iteratively find roots of equations. Starting with x = 2, the calculations yield the next approximation as 1.694, which is the correct answer.

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