We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
386
3
avatar

Find the exact result of:

\((\sqrt{3}-2)^{2017}*(\sqrt{3}+2)^{2018}\)

 

 

edit: my bad, bases aren't the same 

 Dec 22, 2017
edited by Guest  Dec 22, 2017
 #1
avatar
+2

OK! I thought there was more to it than that!.

The exact result is =-(2 + sqrt(3)) - According to "Mathematica 11 Home Edition"

Note: The steps it uses are soooooooo Loooooooooooong, it is rediculous!! There has to be a simpler way of doing it. Maybe somebody else can come up with a short answer.

 Dec 22, 2017
edited by Guest  Dec 22, 2017
 #2
avatar+7354 
+2

\((\sqrt3-2)^{2017}(\sqrt3+2)^{2018} \\~\\ =\,(\sqrt3-2)^{2017}(\sqrt3+2)^{2017}(\sqrt 3+2) \\~\\ =\,[\,(\sqrt3-2)(\sqrt3+2)\,]^{2017}\,(\sqrt3+2) \\~\\ =\,[\,3-4\,]^{2017}\,(\sqrt3+2) \\~\\ =\,[-1]^{2017}\,(\sqrt3+2) \\~\\ =\,(-1)(\sqrt3+2) \\~\\ =\,-\sqrt3-2\)

.
 Dec 22, 2017
 #3
avatar+99275 
+2

Nice, hectiictar!!!!

 

[ This one was a little easier after the edit......LOL!!!  ]

 

 

cool cool cool

 Dec 22, 2017

23 Online Users

avatar
avatar
avatar
avatar