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The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is

  1. $x_{k+1} = 3(x_k+b)/2x_k$

  2. $x_{k+1} = (x_{k}^2+b)/2x_k$

  3. $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$

  4. None of the above

asked in Numerical Methods by Veteran (59.6k points) | 383 views

3 Answers

+2 votes
Best answer
Answer: B

$x_{k+1} = x_k - \frac{f(x_k)}{f'(x)} = x_k - \frac{(x_k^2 - b)}{2x_k} = \frac{2x^2_k - x^2_k + b}{2x_k} = \frac{x^2_k + b}{2x_k}$
answered by Boss (34k points)
0 votes
Answer is D. F(x)=x^2-b. Applying the general formula we can find the answer.
answered by Active (1.2k points)
0 votes

take x= root b

x2=b

f(x)=x2-b

xn+1 = (x2+b) / 2x

answered by Loyal (8.2k points)


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