$\displaystyle y=1/squareroot(x+1)$
$\displaystyle y=x$
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.