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Use Newton's method to approximate a root of the equation x³ + x + 2 = 0 as follows. Let x₁ = 1 be the initial approximation. The second approximation 2 is and the third approximation 3 is (Although these are approximations of the root, enter exact expressions for each approximation.)

Use Newton's method to approximate a root of the equation x³ + x + 2 = 0 as follows. Let x₁ = 1 be the initial approximation. The second approximation 2 is and the third approximation 3 is (Although these are approximations of the root, enter exact expressions for each approximation.)

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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Use Newton's method to approximate a root of the equation x³ + x + 2 = 0 as follows. Let x₁ = 1 be the initial approximation. #1 The second approximation 2 is and the third approximation 3 is (Although these are approximations of the root, enter exact expressions for each approximation.)
Transcribed Image Text:Use Newton's method to approximate a root of the equation x³ + x + 2 = 0 as follows. Let x₁ = 1 be the initial approximation. #1 The second approximation 2 is and the third approximation 3 is (Although these are approximations of the root, enter exact expressions for each approximation.)
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