# GATE1995-2.15

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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

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

take x= root b

x2=b

f(x)=x2-b

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

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