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Simplifying the root of a quadratic

• To: mathgroup at smc.vnet.net
• Subject: [mg63906] Simplifying the root of a quadratic
• From: carlos at colorado.edu
• Date: Sat, 21 Jan 2006 01:50:59 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Consider

etaC=(-48*A0^2-4*A1^2+4*A2^2+
   Sqrt[768*A0^2*A2^2+(48*A0^2+4*A1^2-4*A2^2)^2])/(96*A0*A2);

Neither Simplify nor FullSimplify (with or without assumptions
on the A's) were able to produce the simpler form

etaC=(-12*A0^2-A1^2+A2^2+
   Sqrt[48*A0^2*A2^2+(12*A0^2+A1^2-A2^2)^2])/(24*A0*A2);

which I had to do finally by hand.

Why?

• Follow-Ups:
  • Re: Simplifying the root of a quadratic
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>