Question 1087964
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{{{9/x^4}}} + {{{8/x^2}}} = 1


<pre>
The standard method to solve it is THIS:


1.  Introduce new variable u = {{{1/x^2}}}.

    Then your equation takes the form

    {{{9u^2 + 8u - 1}}} = 0.

    Factor left side polynomial. You will get

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

    The roots are  u = {{{1/9}}}  and  u = -1.


2.  Now return to the original  variable x.

    With the root  u = {{{1/9}}}  you have  {{{1/x^2}}} = {{{1/9}}},

         which implies x = +/- 3.


    With the root  u = -1  you have  {{{1/x^2}}} = -1,

        which HAS NO real solutions.


<U>Answer</U>.  The given equation has two real solutions x = 3 and x = -3.
</pre>

Solved.