The equation f(x) = 0 has a root at x = . Show that rewriting the equation as x = x + f(x), where

The equation f(x) = 0 has a root at x = α. Show that rewriting the equation as x = x + λf(x), where λ is a constant, yields a convergent iteration for a if λ = –1/f´(x₀) and x₀ is sufficiently close to a. Use this method to devise an iteration for the root near x = 2 of the equation x³ – 2x – 1 = 0.