CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1 · Question Q30

Given that the n^{\text{th}} approximation of the root of the equation x^5 = x^3 + 25 based on the Newton-Raphson method is x_n, then x_{n+1} may be expressed as

1. (A)\frac{x_n - x_n^5 - x_n^3 + 25}{5x_n^4 - 3x_n^2}
2. (B)\frac{x_n - x_n^5 - 5x_n^3 - 25}{5x_n^4 - 3x_n^2}
3. (C)\frac{4x_n^5 - 4x_n^3 - 25}{5}
4. (D)\frac{4x_n^5 - 2x_n^3 + 25}{5x_n^4 - 3x_n^2}