GATE | GATE-CS-2002 | Question 40

The Newton-Raphson iteration X_{n + 1} = (X_n/2) + 3/(2X_n) can be used to solve the equation
(A) X² = 3
(B) X³ = 3
(C) X² = 2
(D) X³ = 2

Answer: (A)
Explanation: In Newton-Raphson’s method, We use the following formula to get the next value of f(x). f'(x) is derivative of f(x).

Option (A)

X2 = 3
f(x) = X2 - 3

Xn + 1 = Xn - (Xn2 - 3) / (2*Xn)
  =  (Xn/2) + 3/(2xn) 

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