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

A and B are points on the graph y=x²+8x+7
C and D are points on the graph y=-x²+8x-7
and ABCD is a square.

Find all possible x-coordinates of point A

See The Solution Submitted by Jer

Rating: 4.0000 (1 votes)

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re(2): computer exploration (there is a 4th. a hint)

| Comment 3 of 6 |

(In reply to re: computer exploration (possible spoiler) -- two more squares by Charlie)

There are 4 solutions. Charlie has found 3 via some hard crunching but there is a not-so-difficult analytic solution.

Hint:
The two parabolas are rotations of each about the origin. This puts some limitations on the square.

Posted by Jer on 2010-02-26 15:01:36

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