Ineed this ! 15 points the sum of square of a number and square of its reciprocal 82/9. find the number

Let the number be n.

Then:

n^2 + (1/n)^2 = 82/9; find n.  Find the LCD; it is 9n^2.

Mult all 3 terms by 9n^2:
                                                                  82*9n^2
9n^4 + 9 = (82/9)(9n^2)  =>    9n^4 + 9 =   
                                                                        9
Then 9n^4 - 82n^2 + 9 = 0

I used my graphing calculator to find that n = 3.  

Let's check:     is 3^2 + (1/3)^2 = 82/9?
                        Is   9   + 1/9 = 82/9?
                        Is  81 + 1 = 82?   YES.  So, n=3 is a solution.