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Use Newton's method to approximate a root of the equation 5x³ + 6x + 4 = 0 as follows. Let x₁ = - 1 be the initial approximation. The second approximation 2 is and the third approximation x3 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 5x³ + 6x + 4 = 0 as follows. Let x₁ = - 1 be the initial approximation. The second approximation 2 is and the third approximation x3 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 \(5x^3 + 6x + 4 = 0\) as follows. Let \(x_1 = -1\) be the initial approximation. The second approximation \(x_2\) is \(\boxed{\phantom{x}}\), and the third approximation \(x_3\) is \(\boxed{\phantom{x}}\). (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 \(5x^3 + 6x + 4 = 0\) as follows. Let \(x_1 = -1\) be the initial approximation. The second approximation \(x_2\) is \(\boxed{\phantom{x}}\), and the third approximation \(x_3\) is \(\boxed{\phantom{x}}\). (Although these are approximations of the root, enter exact expressions for each approximation.)
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