i) Show that the cubic equation x³ + 5x − 5 = 0 can be rearranged to give: Xn+1 = 5 xn²+5 Solve this cubic equation by iteration. Start with x = 1 and find the value of x to 3 significant figures. You must show your first four values for the iteration giving each to 3 significant figures.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
Problem 16WE
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i)
4.3 Solve polynomial equations by iteration
Show that the cubic equation x³ + 5x − 5 = 0 can be
rearranged to give:
Xn+1 =
5
xn²+5
Solve this cubic equation by iteration. Start with x = 1 and find the value
of x to 3 significant figures. You must show your first four values for the
iteration giving each to 3 significant figures.
X₁ =
X₂ =
X3 =
X4 =
X5 =
X =
Transcribed Image Text:i) 4.3 Solve polynomial equations by iteration Show that the cubic equation x³ + 5x − 5 = 0 can be rearranged to give: Xn+1 = 5 xn²+5 Solve this cubic equation by iteration. Start with x = 1 and find the value of x to 3 significant figures. You must show your first four values for the iteration giving each to 3 significant figures. X₁ = X₂ = X3 = X4 = X5 = X =
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