November 9th, 2016, 05:19 AM  #31 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,467 Thanks: 575 
Amen.

November 11th, 2016, 03:49 PM  #32 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 360 Thanks: 68  
November 12th, 2016, 01:07 AM  #33 
Global Moderator Joined: Dec 2006 Posts: 16,604 Thanks: 1201 
As x and y are the zeros of u²  4u + 5, 1/x and 1/y are the zeros of 5v²  4v + 1, and so their sum is 4/5.

November 15th, 2016, 11:00 PM  #34 
Banned Camp Joined: Nov 2016 From: St. Louis, Missouri Posts: 28 Thanks: 4 Math Focus: arithmetic, fractions 
Although this problem is impossible to solve, you can make things easier in the future by making it so that the solution of x+y is larger than that for x times y.

November 16th, 2016, 03:58 AM  #35 
Global Moderator Joined: Dec 2006 Posts: 16,604 Thanks: 1201 
That doesn't make sense.

November 16th, 2016, 05:12 AM  #36 
Senior Member Joined: May 2008 Posts: 169 Thanks: 33  
December 1st, 2016, 01:43 AM  #37 
Member Joined: Sep 2016 From: India Posts: 81 Thanks: 25 
$x+y=4...........(1)$ $xy=5.............(2)$ dividing eq(1) by $xy$ $\dfrac{x}{xy}+\dfrac{y}{xy}=\dfrac{4}{xy}$ $\dfrac{1}{y}+\dfrac{1}{x}=\dfrac{4}{xy}$ since $xy=5$ therefore, $\dfrac{1}{y}+\dfrac{1}{x}=\dfrac{4}{5}$ 

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