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December 16th, 2017, 07:18 PM  #1 
Newbie Joined: Feb 2012 Posts: 19 Thanks: 0  Anyone can find the roots of this quadratic equation?
$\displaystyle 2a^{2}+2b^{2}c^{2}+12bck +19k^{2}2bc\cdot\sqrt{k\cdot\left(4bc+5k\right)}7k\cdot\sqrt{k\cdot\left(4bc+5k\right)}+2a\cdot(2bc5k+\sqrt{k\cdot\left(4bc+5k\right)})=0$ Here a,b,c>0, and a>bc. I want to find the solution of k as a function of (a, b, c). Anyone can help? Thanks. Last edited by loveinla; December 16th, 2017 at 07:28 PM. 
December 16th, 2017, 07:28 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,854 Thanks: 1078 Math Focus: Elementary mathematics and beyond 
I don't think it's quadratic. Have you tried plugging it in to an online CAS (Computer Algebra System), such as Wolfram Alpha?

December 17th, 2017, 07:30 AM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 608 Thanks: 82 
Can a quadratic equation have more than two variables?

December 17th, 2017, 09:04 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,115 Thanks: 913 
Yikes...one of ugliest equation I've seen! OK; here's a similar "less complicated" ugly one: k^2 + k + sqrt(ak)  sqrt(bk)  sqrt(ck) = 0 Go here to see solutions: http://www.wolframalpha.com/input/?i...k)+%3D+0+for+k Ready to quit?! Last edited by Denis; December 17th, 2017 at 09:09 AM. 
December 17th, 2017, 01:19 PM  #5 
Senior Member Joined: May 2016 From: USA Posts: 1,122 Thanks: 466  
December 17th, 2017, 01:19 PM  #6  
Senior Member Joined: May 2016 From: USA Posts: 1,122 Thanks: 466  Quote:
 
December 17th, 2017, 01:31 PM  #7 
Global Moderator Joined: May 2007 Posts: 6,582 Thanks: 610 
The square root expression is the same in all the terms containing it, so it can be factored out. Put the square root containg term on one side of the equation and the rest on the other side. Square both sides and you have a fourth degree polynomial in k.


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