SOLUTION: 12(x^2+1/x^2)-56(x+1/x)+89=0

Question 877681: 12(x^2+1/x^2)-56(x+1/x)+89=0

Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

Let 

Then

    

    

    

So substitute  for 
and  for 









6u - 13 = 0;       2u - 5 = 0
     6u = 13           2u = 5
      u =          u =

For u = , since 



Multiply through by 6x





(3x-2)(2x-3) = 0

3x-2 = 0;     2x-3 = 0
  3x = 2;       2x = 3 
   x = ;       x = 


------


For u = , since 



Multiply through by 2x





(2x-1)(x-2) = 0

2x-1 = 0;      x-2 = 0
  2x = 1;        x = 2 
   x = ;       

So there are four solutions:

x = 
x = 
x = 
x = 2

Edwin

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