Rearrange the equation x=F(x) into the form f(x)=0, where f is a polynomial function.

(I'm writing it up, so hold on)

Question

Rearrange the equation x=F(x) into the form f(x)=0, where f is a polynomial function.

(I'm writing it up, so hold on)

anonymous · Answer

$$X_{0}=0, ~~~X_{r+1}= \sqrt[11]{x_{r}~^7-6}$$

anonymous · Answer

raise both sides to the power of 11
subtract x^7 
add 6

anonymous · Answer

$$x=\sqrt[11]{x^7-6}$$
$$x^{11}=x^7-6$$
$$x^{11}-x^7+6=0$$

anonymous · Answer

Thanks so much :)

anonymous · Answer

easy once you see it right?

anonymous · Answer

Yes! The next step is to use the iteration, with the given initial approximation x_0 to find the terms of the sequence x_0, x_1,..... As far as x_5?

anonymous · Answer

$$x_0, x_1,..... As ~far~ as~~~ x_5$$?

anonymous · Answer

@satellite73

anonymous · Answer

i think for this you use 
$$x_{n+1}=F(x_n)$$

anonymous · Answer

Ok, and how do you apply the formula?

anonymous · Answer

need a calculator for sure

anonymous · Answer

you have 
$$x_{n+1}=\sqrt[11]{x^7-6},x_0=0$$ so 
$$x_1=\sqrt[11]{0^7-6}=\sqrt[11]{-6}$$ whatever that is

anonymous · Answer

i get 
$$x_1=-1.1769$$ rounded

anonymous · Answer

It shows the answer in decimals. Yes, that's the answer. but I can't get that on my calculator? How did you get it?

anonymous · Answer

and then 
$$x_2=\sqrt[11]{(-1.1769)^7-6}$$etc

anonymous · Answer

depends on your calculator

anonymous · Answer

Casio scientific

anonymous · Answer

i used a cheap one, but if you have a nice one you can take 
$$(-6)^{\frac{1}{11}}$$

anonymous · Answer

anonymous · Answer

Mine gives -1.0859? Why?

anonymous · Answer

maybe i am wrong

anonymous · Answer

anonymous · Answer

no i think i am right

anonymous · Answer

Yes. I got it now. Thanks :) I made a mistake... I shouldn't have added the - until after I calculated the square.

anonymous · Answer

ok good!  you have four more to do good luck

anonymous · Answer

Thanks again! :D