If 2x-6=2/x then (x^2)+(1/x^2)=?

Question

Its options are a)11 

                           b)3 

                            c)9

                            d)1

Answer 1

Solve the first equation by 'clearing fractions' to get 2x² - 6x = 2  or  x² - 3x - 1 = 0.  (You could find the roots using quadratic formula; they'll be irrational)

 

So x² = 1+3x and so the expression    (x²)+(1/x²)= 1+3x + 1/(1+3x).  Play around further with exact or decimal answers, if you wish.