1. ## Very eerie result.

Solve analytically for the intersections of

$y=4-\frac{x^4}{64}$

and

$y=\sqrt{16-x^2}$

I'm concerned solely with the intersection in the first quadrant. Please tell em your result. I want to know if I'm just crazy when I see mine. You will know what I'm talking about when you solve it.

2. x^4 = 256

and

x^2 = 16

3. I'm talking about the one between 0 and 4

4. Originally Posted by Keithfert488
I'm talking about the one between 0 and 4

I get $x= 0$

5. $x=2\sqrt{2\sqrt{5}-2}$

6. I am talking about the solution where x is greater than 0 and less than 4

7. Originally Posted by Stroodle
$x=2\sqrt{2\sqrt{5}-2}$
what I find so eerie is how close this is to pi. Is it just a coincidence?

8. Oh, I wouldn't have a clue But I'd say it's probably just a coincidence...

9. The reason I did this is because I was trying to solve for the intersection of a fourth root polynomial with y-intercept r and zeros -r and r and a circle centered at the origin with radius r. So the x-coordinate of that intersection is very close to $\frac{r\pi}{4}$