SOLUTION: Find the real roots of the equation 9/x^4+8/x^2=1

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Question 1087964: Find the real roots of the equation 9/x^4+8/x^2=1
Found 3 solutions by math_helper, MathTherapy, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
and

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

USE PARENTHESES if you want a correct answer!
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
+ = 1 

The standard method to solve it is THIS:


1.  Introduce new variable u = .

    Then your equation takes the form

     = 0.

    Factor left side polynomial. You will get

    (9u -1)*(u+1) = 0.

    The roots are  u =   and  u = -1.


2.  Now return to the original  variable x.

    With the root  u =   you have   = ,

         which implies x = +/- 3.


    With the root  u = -1  you have   = -1,

        which HAS NO real solutions.


Answer.  The given equation has two real solutions x = 3 and x = -3.

Solved.



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