SOLUTION: May I have some help with the following equation? (x+1/x)^2 + 4(x+1/x)+ 3=0

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Question 121819: May I have some help with the following equation?
(x+1/x)^2 + 4(x+1/x)+ 3=0
Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
Let z=x+1/x then z^2+4z+3=0 then z=-1 or -3 then
x+1/x =-1 or x+1/x=-3
if x+1/x = -1 then x^2+1=-x then x^2+x+1=0 ( no real solution)
if x+1/x = -3 then x^2+1=-3x then x^2+3x+1=0 then
x=(-3+sqrt(5))/2 or
x=(-3-sqrt(5))/2