anonymous
  • anonymous
Use Newton's method to find an approximate solution for the equation x^2+x=3 Start with x0=1 and iterate Newton's method twice to find x2.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
f' = 2x + 1 f(0) = -3 x1 = x0 - f(0) / f'(0) shoot - i'm not sure thats right - i'll have to check
anonymous
  • anonymous
I am also not sure, if you find anything about it pls post it
amistre64
  • amistre64
newtons method is finding the equation of the tangent line; getting its root for a new x value to repeat the iteration right?

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amistre64
  • amistre64
Xn = f'(x)(x-x0)+y0 = 0
anonymous
  • anonymous
I think so
amistre64
  • amistre64
(1,2) Xn = (2(1)+1)(x-1)+2
amistre64
  • amistre64
Xn = 3x - 1; Xn = 1/3 then right?
anonymous
  • anonymous
what do you label as Xn?
amistre64
  • amistre64
new X value; Xn just seemed appropriate
anonymous
  • anonymous
ok
amistre64
  • amistre64
I coulda went with Larry, but.... i know a cucumber named Larry lol
anonymous
  • anonymous
:)
anonymous
  • anonymous
sorry still not clear, I am just working it out, but I dont see how you get y0=2
amistre64
  • amistre64
x^2 +x = 3 is that a typo?
amistre64
  • amistre64
x^2 +x +3 maybe?
anonymous
  • anonymous
that is it
anonymous
  • anonymous
first one
amistre64
  • amistre64
x^2 +x = 3 ; when x=1 this is simply a false statement then 1+1 = 3???
anonymous
  • anonymous
yep but the method will tend to the right answer
amistre64
  • amistre64
x^2 +x -3 = 0 then
anonymous
  • anonymous
that is the same
amistre64
  • amistre64
then remove the 0 to find some solutions
amistre64
  • amistre64
when x = 1; y = ? (1,-1) then right?
anonymous
  • anonymous
-1 right
amistre64
  • amistre64
use this point for your tangent equation that follows: y-y0 = m(x-x0) y = m(x-x0)+y0
amistre64
  • amistre64
m = f'(x)
amistre64
  • amistre64
y = (2(1)+1)(x-1)-1
anonymous
  • anonymous
clear
amistre64
  • amistre64
y = 3x-4; the root is x = 4/3 then right?
anonymous
  • anonymous
that is why i did not see how that 2 appeared
amistre64
  • amistre64
:) right concept, wrong thought lol
anonymous
  • anonymous
right and I should do this again to get the result, thanks for the help!
amistre64
  • amistre64
youre welcome :)
anonymous
  • anonymous
A mathematica solution with comments. Refer to the pdf attachment.
1 Attachment
anonymous
  • anonymous
andras:what/where are you studying?
anonymous
  • anonymous
pure maths, just finished 1st year
anonymous
  • anonymous
are you on facebook? pardon me if posting this here is a breach of ettiquet
anonymous
  • anonymous
:) I dont mind. Yes I am on facebook
anonymous
  • anonymous
you can add me if you wish but I dont use facebook that often. Andras Honyek
anonymous
  • anonymous
will do...I just sent you a request...neat...most people i know are glued to their fb accounts.

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