square root function

**Veronica1999** · September 16th 2011, 03:23 PM

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

**CaptainBlack** · September 16th 2011, 09:32 PM

Originally Posted by Veronica1999

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

The $x$ coordinate is the solution of the equation $f(x)=x$ which may be expanded:

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

and again:

$1996x=x^4$

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

$x^4-1996x=0$

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

$x^4-1996x=0$

CB

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