(x+2/x)^2+9(x+2/x)+18=0

Question

Find all the real solutions of the equation.

Answer 1

Let    q = (x + 2/x)

 

 

q² + 9q + 18 = 0

 

 

Factor using FOIL.

 

(q + 3)(q + 6) = 0

 

q = -3         and          q = -6

 

 

Substitute these values of q into the original substitution.

 

(x + 2/x) = -3          and             (x + 2/x) = -6

 

 

Solve for x from these two equations.