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I have the expression:

$$-\left(\frac{A}{3a} + \frac{B}{3b} + \frac{C}{3c}\right) \pm \frac{8}{3} \sqrt{b^{2}c^{2}A^{2} + a^{2}c^{2}B^{2} + a^{2}b^{2}C^{2} - abc^{2}AB - ab^{2}cAC - a^{2}bcBC}$$

and I would like to be able to simplify it, if it is at all possible.

Thank you.

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    $\begingroup$ "Equation" is the wrong word here. "Expression" would fit. $\endgroup$ – Michael Hardy Jun 14 '15 at 16:26
  • $\begingroup$ @MichaelHardy Ah, I see. I will edit the post appropriately. Thank you for the advice. $\endgroup$ – Taylor Jun 14 '15 at 16:27
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$$-\left(\frac{A}{3a} + \frac{B}{3b} + \frac{C}{3c}\right) \pm \frac{8}{3} \sqrt{{a^2b^2c^2}\left(\frac{A^2}{a^2} +\frac{B^2}{b^2} + \frac{C^2}{c^2} - \frac{AB}{ab} - \frac{AC}{ac} - \frac{BC}{bc}\right)},$$

$$-\left(\frac{A}{3a} + \frac{B}{3b} + \frac{C}{3c}\right) \pm \frac{8|abc|}{3} \sqrt{\frac{A^2}{a^2} +\frac{B^2}{b^2} + \frac{C^2}{c^2} - \frac{AB}{ab} - \frac{AC}{ac} - \frac{BC}{bc}},$$

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  • $\begingroup$ Wow, that is really neat! Thank you, @Essam. However, is this as far as one can simplify the expression, in your opinion? $\endgroup$ – Taylor Jun 14 '15 at 16:44
  • $\begingroup$ @RaymondManzoni Oh, so is this incorrect? $\endgroup$ – Taylor Jun 14 '15 at 16:45
  • $\begingroup$ @RaymondManzoni Ah, I see. $\endgroup$ – Taylor Jun 14 '15 at 16:47

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