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Could I have some quick help with this? 

 

If x satisfies (x^2) + (3x + (3/x) + (1)/(x^2) = 26 and x can be written as a+ (sqrt(b)) where a and b are positive integers, then find a + b.

 

I accidentally made it off-topic :p. Whoops

Guest Jun 18, 2017
edited by Guest  Jun 18, 2017
edited by Guest  Jun 18, 2017
edited by Guest  Jun 18, 2017
 #1
avatar+87319 
+1

 

x^2 +  ( 3x + (3/x)  + (1/x^2) )  =  26   multiply through by x^2

 

x^4 + 3x^3 + 3x + 1 =  26x^2   simplify

 

x^4 + 3x^3 - 26x^2 + 3x + 1  =  0

 

There are 4 real solutions....they are....

 

2 + sqrt (7)   and  2 - sqrt (7)    the sum of these is  4

 

-7/2 +  (3sqrt (5) ) / 2      and  -7/2 -  (3sqrt(5) ) / 2      the sum of these is  -7

 

 

cool cool cool

CPhill  Jun 18, 2017
 #2
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Thanks!

Guest Jun 18, 2017

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