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