The Newton-Raphson iteration xn+1 = xn/2 + 3/(2xn) can be used to solve which…
2002
The Newton-Raphson iteration xn+1 = xn/2 + 3/(2xn) can be used to solve which equation?
- A.
x² = 3
- B.
x³ = 3
- C.
x² = 2
- D.
x³ = 2
Show answer & explanation
Correct answer: A
Newton-Raphson for f(x) = 0 is x_(n+1) = x_n - f(x_n)/f'(x_n). If the equation is x² = 3, then f(x) = x² - 3 and f'(x) = 2x.
So x_(n+1) = x_n - (x_n² - 3)/(2x_n) = (2x_n² - x_n² + 3)/(2x_n) = x_n/2 + 3/(2x_n).
This matches the given iteration. Hence the equation is x² = 3.