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 December 19th, 2008, 10:18 AM #1 Newbie   Joined: Dec 2008 Posts: 11 Thanks: 0 roots and equation Hi! I've got a problem with: Proof that $\sqrt{5+\sqrt{21}} + \sqrt{8+\sqrt{55}}= \sqrt{7+\sqrt{33}} + \sqrt{6+\sqrt{35}}$ Thanks a lot for help!
 December 22nd, 2008, 01:28 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,370 Thanks: 2007 $\frac{3}{\sqrt6}\,+\,\sqrt{7/2}\,+\,\frac{5}{\sqrt{10}}\,+\,\sqrt{11/2}\,=\,\frac{3}{\sqrt6}\,+\,\sqrt{11/2}\,+\,\frac{5}{\sqrt{10}}\,+\,\sqrt{7/2}$ $\sqrt{\left(\frac{3}{\sqrt{6}}\,+\,\sqrt{7/2}\right)^2}\,+\,\sqrt{\left(\frac{5}{\sqrt{10}}\, +\,\sqrt{11/2}\right)^2}\,=\,\sqrt{\left(\frac{3}{\sqrt6}\,+\, \sqrt{11/2}\right)^2}\,+\,\sqrt{\left(\frac{5}{\sqrt{10}}\, +\,\sqrt{7/2}\right)^2}$ Your equation follows.

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