Brainlag PlusRearrange an equation into x = g(x), then feed each answer back in until the values settle on a root.
Feed the answer back in
x³ + 2x − 7 = 0 can be rearranged to x = ∛(7 − 2x).
That suggests the iteration
x₍ₙ₊₁₎ = ∛(7 − 2xₙ)
Start with x₀ = 1: x₁ = ∛5 = 1.7100, x₂ = ∛3.5800 = 1.5299, x₃ = 1.6143, ... The values close in on the root, 1.5946... On a calculator: type 1, press =, then type ∛(7 − 2Ans) and press = again and again.
The rest of this lesson and its 7 practice questions are in Plus.
Screen 1 of 3, free to read.
- 7 exam-style questions, marked as you go, each with a worked solution
- The Numerical methods simulation beside every question
- Anything you get wrong is saved to your flashcards