BMAD Posted July 3, 2013 Report Share Posted July 3, 2013 Evaluate the following expression sqrt(2+sqrt(2+sqrt(2+sqrt(2+... repeating forever. Quote Link to comment Share on other sites More sharing options...
0 BobbyGo Posted July 3, 2013 Report Share Posted July 3, 2013 2? Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted July 3, 2013 Author Report Share Posted July 3, 2013 2? correct. Care to explain your solution? Quote Link to comment Share on other sites More sharing options...
0 BobbyGo Posted July 3, 2013 Report Share Posted July 3, 2013 2? correct. Care to explain your solution? Calculator. Every +sqrt(2) I pasted into the equation returned an answer that edged closer and closer to 2. It was more of a guess than an answer. Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted July 3, 2013 Author Report Share Posted July 3, 2013 let x = sqrt(2+sqrt(2+sqrt(2+sqrt(2+... then ... Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted July 4, 2013 Report Share Posted July 4, 2013 let x = sqrt(2+sqrt(2+sqrt(2+sqrt(2+... then ... I hope you're not intimating that -1 is also a solution! Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted July 4, 2013 Author Report Share Posted July 4, 2013 (edited) let x = sqrt(2+sqrt(2+sqrt(2+sqrt(2+... then ... I hope you're not intimating that -1 is also a solution! nice work, but clearly -1 is a false solution and should be disregarded as such leaving only 2 Edited July 4, 2013 by BMAD Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted July 4, 2013 Author Report Share Posted July 4, 2013 to expand on superprismatic let x = sqrt(2+sqrt(2+sqrt(2+sqrt(2+... so x = sqrt(2 + x) x^2 = 2 + x x^2 - x - 2 = 0 (x-2)(x+1) = 0 x =2, x =-1 x=-1 is impossible as the sqrt cannot give a negative answer (i.e. -1 = sqrt(1)) Quote Link to comment Share on other sites More sharing options...
Question
BMAD
Evaluate the following expression
sqrt(2+sqrt(2+sqrt(2+sqrt(2+... repeating forever.
Link to comment
Share on other sites
7 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.