GATE CSE 1995 | Question: 2.15

Question

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

• A. $x_{k+1} = 3(x_k+b)/2x_k$

• B. $x_{k+1} = (x_{k}^2+b)/2x_k$

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

• D. None of the above

Answer 1

Answer: B

$x_{k+1} = x_k - \frac{f(x_k)}{f'(x)} = x_k - \frac{(x_k^2 - b)}{2x_k} = \frac{2x^2_k - x^2_k + b}{2x_k} = \frac{x^2_k + b}{2x_k}$

Answer 2

Answer is D. F(x)=x^2-b. Applying the general formula we can find the answer.

Comments

No answer is only B...

Answer 3

take x= root b

x²=b

f(x)=x²-b

x_n+1 = (x²+b) / 2x