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10. The equation 2x³ + x² - 1 = 0 has exactly one real root. (a) Show that, for this equation, the Newton-Raphson formula can be written Xn+1 = 4x2 + x² + 1 6x2 + 2xn Using the formula given in part (a) with ₁ = 1 (b) find the values of x2 and 3 (c) Explain why, for this question, the Newton-Raphson method cannot be used with r.

10. The equation 2x³ + x² - 1 = 0 has exactly one real root. (a) Show that, for this equation, the Newton-Raphson formula can be written Xn+1 = 4x2 + x² + 1 6x2 + 2xn Using the formula given in part (a) with ₁ = 1 (b) find the values of x2 and 3 (c) Explain why, for this question, the Newton-Raphson method cannot be used with r.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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10. The equation 2x³ + x² - 1 = 0 has exactly one real root. (a) Show that, for this equation, the Newton-Raphson formula can be written 4x³ + x² + 1 η Xn+1 = 6x2 + 2xn Using the formula given in part (a) with x₁ (b) find the values of x2 and x3 (c) Explain why, for this question, the Newton-Raphson method cannot be used with x₁ = 0. 2 - 1
Transcribed Image Text:10. The equation 2x³ + x² - 1 = 0 has exactly one real root. (a) Show that, for this equation, the Newton-Raphson formula can be written 4x³ + x² + 1 η Xn+1 = 6x2 + 2xn Using the formula given in part (a) with x₁ (b) find the values of x2 and x3 (c) Explain why, for this question, the Newton-Raphson method cannot be used with x₁ = 0. 2 - 1
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