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# Help?

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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
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#1
+84239
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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

CPhill  Jun 18, 2017
#2
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Thanks!

Guest Jun 18, 2017

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