Show that the equation x3+4x=1x^3 + 4x = 1x3+4x=1 has a solution between x=0x = 0x=0 and x=1x = 1x=1.
Show that the equation x3+4x=1x^3 + 4x = 1x3+4x=1 can be rearranged to give: x=14−x34\displaystyle x = \frac{1}{4} - \frac{x^3}{4}x=41−4x3
Starting with x0=0x_0 = 0x0=0, use the iteration formula xn+1=14−xn34\displaystyle x_{n+1} = \frac{1}{4} - \frac{x_n^3}{4}xn+1=41−4xn3 twice to find an estimate for the solution to x3+4x=1x^3 + 4x = 1x3+4x=1
Practise Edexcel GCSE Maths Iteration with exam-style questions for Foundation and Higher tier. 40 questions, matched to the Edexcel GCSE Maths (1MA1) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.