Hmm...I can't see what the significance of the the first quadrant point is...

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- Sep 16th 2011, 03:23 PMVeronica1999square root function
Hmm...I can't see what the significance of the the first quadrant point is...

- Sep 16th 2011, 09:32 PMCaptainBlackRe: square root function
The $\displaystyle x$ coordinate is the solution of the equation $\displaystyle f(x)=x$ which may be expanded:

$\displaystyle \sqrt{1996x}=x^2$

and again:

$\displaystyle 1996x=x^4$

(but now we need to remember that $\displaystyle x\ge 0$) and rearranging we have:

$\displaystyle x^4-1996x=0$

which by Descartes rule of signs has exactly one positive root. So the $\displaystyle x$ coordinate of the point of intersection is the unique positive root of the quartic:

$\displaystyle x^4-1996x=0$

CB