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

edited by Guest Jun 18, 2017

edited by Guest Jun 18, 2017

#1**+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

CPhill
Jun 18, 2017