Question

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.

Answer 1

f' = 2x + 1
f(0) = -3
x1 = x0 - f(0) / f'(0)

shoot - i'm not sure thats right - i'll have to check

Answer 2

I am also not sure, if you find anything about it pls post it

Answer 3

newtons method is finding the equation of the tangent line; getting its root for a new x value to repeat the iteration right?

Answer 4

Xn = f'(x)(x-x0)+y0 = 0

Answer 5

I think so

Answer 6

(1,2)

Xn = (2(1)+1)(x-1)+2

Answer 7

Xn = 3x - 1; Xn = 1/3 then right?

Answer 8

what do you label as Xn?

Answer 9

new X value; Xn just seemed appropriate

Answer 10

ok

Answer 11

I coulda went with Larry, but.... i know a cucumber named Larry lol

Answer 12

:)

Answer 13

sorry still not clear, I am just working it out, but I dont see how you get y0=2

Answer 14

x^2 +x = 3 is that a typo?

Answer 15

x^2 +x +3 maybe?

Answer 16

that is it

Answer 17

first one

Answer 18

x^2 +x = 3 ; when x=1 this is simply a false statement then

1+1 = 3???

Answer 19

yep but the method will tend to the right answer

Answer 20

x^2 +x -3 = 0 then

Answer 21

that is the same

Answer 22

then remove the 0 to find some solutions

Answer 23

when x = 1; y = ?

(1,-1) then right?

Answer 24

-1 right

Answer 25

use this point for your tangent equation that follows:

y-y0 = m(x-x0)

y = m(x-x0)+y0

Answer 26

m = f'(x)

Answer 27

y = (2(1)+1)(x-1)-1

Answer 28

clear

Answer 29

y = 3x-4; the root is x = 4/3 then right?

Answer 30

that is why i did not see how that 2 appeared

Answer 31

:) right concept, wrong thought lol

Answer 32

right and I should do this again to get the result, thanks for the help!

Answer 33

youre welcome :)

Answer 34

A mathematica solution with comments. Refer to the pdf attachment.

Answer 35

andras:what/where are you studying?

Answer 36

pure maths, just finished 1st year

Answer 37

are you on facebook?
pardon me if posting this here is a breach of ettiquet

Answer 38

:) I dont mind. Yes I am on facebook

Answer 39

you can add me if you wish but I dont use facebook that often. Andras Honyek

Answer 40

will do...I just sent you a request...neat...most people i know are glued to their fb accounts.