Squares joining quadratics (Posted on 2010-02-24)

	Submitted by Jer
Rating: 4.0000 (1 votes)
Solution:	(Hide)
Any square must be centered at the origin. Therefore B is the image of A rotated by 90 degrees about the origin. (C and D will work themselves out.) A=(x,x2+8x+7) B=(-x2-8x-7,x) but since B is also on the first parabola we can substitute this point into the first equation which simplifies into the quartic 0 = x4+16x3+70x2+47x Which has 4 real roots: x={0, -.8157899, -7.756981, 7.427229}

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2024-04-28 22:16:58
	re: Four squares by analysis (spoiler)	Jer	2011-02-12 19:10:06
	Four squares by analysis (spoiler)	Harry	2010-02-27 02:05:46
	re(2): computer exploration (there is a 4th. a hint)	Jer	2010-02-26 15:01:36
	re: computer exploration (possible spoiler) -- two more squares	Charlie	2010-02-24 18:26:20
	computer exploration (possible spoiler)	Charlie	2010-02-24 13:04:26