hp 50 g simplify solutions
08-09-2015, 02:24 PM
Post: #1
 peacecalc Member Posts: 187 Joined: Dec 2013
hp 50 g simplify solutions
Hello friends,

on hpcalc.org there exist a nice little libary which makes it possible, that the hp 50g is able to solve exact equations of 4th order.

For instance: $x^4 - 16 = 0$

Okay it is very easy and even the hp 50g is able to factorize it, but that is not the point. The program "polyroot" gives a list with four entries. One of the entries looks like:

$\frac{1}{6\cdot \sqrt{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{- \left(3+3\cdot i\cdot \sqrt{3}\right)\cdot {\sqrt{\frac{8\cdot \sqrt{3}}{9}}}^{3}-\left(4-4\cdot i\cdot \sqrt{3}\right)\cdot \sqrt{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{6}-\frac{1}{6\cdot \sqrt{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{- \left(3-3\cdot i\cdot \sqrt{3}\right)\cdot {\sqrt{\frac{8\cdot \sqrt{3}}{9}}}^{3}-\left(4+4\cdot i\cdot \sqrt{3}\right)\cdot \sqrt{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{6} \\ -\frac{1}{3\cdot \sqrt{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{3\cdot {\sqrt{\frac{8\cdot \sqrt{3}}{9}}}^{3}-4\cdot \sqrt{\frac{8\cdot \sqrt{3}}{9}}}\cdot \sqrt{3}$

Holy cow! If you take the command "->NUM" you get the short and expected short answer, but not as a simplified symbolic answer. I test a lot of combinations of the commands "SIMPLIFY" "COLLECT" and with the special commands "EXPLN" and so on.
I hope there is somebody in this universe who knows the trick(s) for reducing such a
monster expression to a simple complex number.