If a - 1/(a - 9) = 26 Then find , (a - 9)2 + 1/((a - 9)^2)

Given = a - \(\frac{1}{a - 9}\) = 26

By subtracting 9 on both sides we get,

(a - 9) - \(\frac{1}{a - 9}\) = 26 - 9 = 17

(a - 9)² + \(\frac{1}{(a - 9)^2}\) = 17² + 2 = 291

 

Note - if x -  \(\frac{1}{x}\) = a

then x² + \(\frac{1}{x^2}\) =  a² + 2