Thread: finding roots of equation

$\displaystyle y=1/squareroot(x+1)$
$\displaystyle y=x$
Sketch the two graphs, and indicate on your graph the location of the root r of the equation $\displaystyle 1/squareroot(x+1)=x$. Use algebra and show that x=r can also solve the equation $\displaystyle x^3+x^2=1$. Calculate r to 5 significant figurees using simple iteration.

Im stuck in the part in bold. I can rearrange $\displaystyle 1/squareroot(x+1)=x$ into $\displaystyle x^3+x^2=1$, but how do i show that x=r can solve the equation? Thanks.

Its just asking you to find a solution for x, in this case we have called it r.

So next step is to solve this $\displaystyle x^3+x^2=1$

Do you know how?

Thanks, do i try to solve $\displaystyle x^3+x^2-1=0$?

If so, Im not really sure how, what do i do to solve it?

Yes thats what you solve.

It mentions above 'using simple iteration'. Do you know this method?

oh right, thanks, i misunderstood the questions, thanks alot!! yeap i know how to do it