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What's your x (on the left-hand side) to the power of?

\[\frac{1}{3x^2}=2x+1 \rightarrow 1=3x^2(2x+1)=6x^3+3x^2\]

he may have meant (1/3)x^2...

Is that what you meant, mac?

that would sound more likely to be the homework assigned to an algebra class

Because solving 6x^3+3x^2=1 algebraically is not nice.

^not at all...

ergh... that still wont give integer roots

You can complete the square or use the quadratic formula.

Can't help that...

\[x^2-6x-3=0 \rightarrow x=3 \pm 2\sqrt{3}\]

as for the 6xcubed i would use long division... or rather synthetic... is that the best way?

Do you mean you would use long division or synthetic after finding a factor?

i would use them to check if i can guess a factor lol

Yes

i wonder where mac went...

Mac's lurking...

newton-raphson method? whats that?

im curious, as the derivative cant tell you solutions... can it??

Check out the image - this is what's going on.
http://en.wikipedia.org/wiki/Newton's_method

thank you man

You're welcome ;)

what the heckkk that is freaking genius. damn newton -.-

Yeah, I think it's his best thing outside of the calculus and Laws of Motion.

i didnt understand the second half of that lol

I'm going to do an example.

You can see after one trial, it's pretty close.

Next one would be 577/408 ~= 1.414215686

dang, the formula, has you divide the tangent line function by the tangent line slope, why?

oh wait i get it...

nope that made no sense... ill figure this out, gimmy a sec

You're half there.

It's difficult to explain online. They need to put a drawing feature in this thing.

lol they do, like tutorvista

I think mac must think his thread's been hijacked.

i think he left

so youre taking x and subtracting y/y'(x)

i still dont get why ><

Hang on, I'll see if I can put a small proof together.

ok :/

And go along with it...

i can understand how it all works, but how does the drawing explain how the formula works?

(i already made a drawring btw lol)

Then repeat...

oh wow that makes sense...

Happy now?

yes :D thanks for spending time to teach me this stuff :O

No worries - it's good you want to know :)

i honestly am really curious as to where mac went...

he stopped observing a while ago even

Yeah, he probably got his answer and was all, "WTF is going on?!"

whats after differential equations?

Eh?

like course wise, you take calc1 calc2 calc3 diff eq then what?

Have no idea man, not American ;D

your degree*

lol, keep going, though!

do you know all that is taught of mathematics to the extent that research is your only option?

anddd man i need help on something:
\[\int\limits_{}^{} (\sin x - \cos x) \div (\sin x)\]

nevermind i got it

Yes, you're right on your last point.

thats pretty crazy, that you know everything O.o

I don't know everything..!

you know everything in math...

No I don't ;)