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August 23rd, 2016, 09:29 AM  #1 
Newbie Joined: Aug 2016 From: india Posts: 2 Thanks: 0  how to find the roots of the following quadratic equation?
x^2+[((a^2))/((a^2+b^2))+((a^2+b^2))/(a^2)]x+1=0 What the roots of the above equation? Last edited by skipjack; August 23rd, 2016 at 10:00 AM. 
August 23rd, 2016, 10:04 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,652 Thanks: 838 
Just use the quadratic formula $a=1$ $b=\dfrac{a^2}{a^2+b^2}+\dfrac{a^2+b^2}{a^2}$ $c=1$ It will be a mess, true. Last edited by skipjack; August 23rd, 2016 at 10:18 AM. 
August 23rd, 2016, 10:17 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,241 Thanks: 1438 
The equation is cluttered with redundant parentheses. It's of the type $\displaystyle x^2 + (p + 1/p)x + 1 = 0$, which factorizes as $\displaystyle (x + p)(x + 1/p) = 0$. $\displaystyle x^2 + \left(\frac{a^2}{a^2 + b^2} + \frac{a^2 + b^2}{a^2}\right)x + 1 = \left(x + \frac{a^2}{a^2 + b^2}\right)\left(x + \frac{a^2 + b^2}{a^2}\right) = 0$ is easy to solve. 
August 24th, 2016, 05:36 AM  #4 
Newbie Joined: Aug 2016 From: india Posts: 2 Thanks: 0 
thanks


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