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fluffylove83

08.04.2021

Mathematics

Approximate solutions are the estimate values of an equation

The approximate solution of the equation is x = 0.45

How to determine the approximate solution

The equation is given as:

x^3 + 2x- 1= 0

The iteration is given as:

$x_{n+1} = \frac{1}{x_n^2 + 2}$

To start with, we have:

x_1 = 1

So, we have:

$x_2 = \frac{1}{1^2 + 2} = \frac 13 =0.33333333$

The next iteration is:

$x_3 = \frac{1}{0.33333333^2 + 2} = 0.47368421102$

The next iteration is:

$x_4 = \frac{1}{0.47368421102^2 + 2} = 0.4495641344$

The next iteration is:

$x_5 = \frac{1}{0.4495641344^2 + 2} = 0.45411035264$

The next iteration is:

$x_6 = \frac{1}{0.45411035264^2 + 2} = 0.45326473189$

Notice that:

x5 and x6 have the same value to 2 decimal places.

i.e. $x_5 \approx x_6 = 0.45$

Hence, the approximate solution of the equation is x = 0.45

Read more about approximate solutions at:

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