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

$\displaystyle y=x$

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.