Can x=r solve the equations 1/squareroot(x+1)=x and x^3+x^2=1?

[gomes.]

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

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


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

 

[tiny-tim]

hi gomes!

(have a square-root: √ and try using the X² icon just above the Reply box )

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

there isn't really anything to prove …

"r is the root of 1/√(x+1) = x" is just another way of saying that 1/√(r+1) = r