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## Homework Statement

I'll try to be as clear as possible but this exercise is in portuguese and this is a free translation from me

"The sum of two numbers is 3.4 .If we take each of them and summed with they square, the product of it would be 18.5856. The lowest of those number is in the interval [1,1.5]Solve it using the Newthon Methot for an error lesser than 10^-2"

## Homework Equations

(deduced by me from the problem)

x+y=3.4

(x+x

^{2})*(y+y

^{2})=18.5856

## The Attempt at a Solution

y=x-3.4

(x+x

^{2})*(x+x

^{2}+x

^{2}+2*x

^{3}+x

^{4})=18.5856

x

^{6}+3*x

^{5}+4*x

^{4}+3*x

^{3}+x

^{2}-18.5865=f(x)

6*x

^{5}+15*x

^{4}+16*x

^{3}+9*x

^{2}+2*x=f'(x)

iterative function = x - f(x)/f'(x)

Am I in the right way? Because if i continue with this I will come to

a really big equation and this exercise looks way simpler than this.

My main concerns are:

1- Are the equation that I provided right for what the problem is asking?

2-Should I have stayed with x and y and solved as a non-linear system? I've made this way because the problem is in a list made for the linear chapter, but it could be an error.

3-If i'm in the right direction, is there a way to simplify this equation in a product of sums ?

thanks in advance!