SOLUTION: Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) (x+6/x)^2 +10(x+6/x)+21=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) (x+6/x)^2 +10(x+6/x)+21=0       Log On


   

Question 911603: Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
(x+6/x)^2 +10(x+6/x)+21=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution.
u=%28x%2B6%29%2Fx
.
.
u%5E2%2B10u%2B21=0
%28u%2B7%29%28u%2B3%29=0
Two "u" solutions:
u%2B7=0
u=-7
%28x%2B6%29%2Fx=-7
x%2B6=-7x%7D%7D%0D%0A%7B%7B%7B-8x=6
highlight%28x=-3%2F4%29
.
.
.
u%2B3=0
u=-3
%28x%2B6%29%2Fx=-3
x%2B6=-3x
-4x=6
highlight%28x=-3%2F2%29