If a - 1/(a - 9) = 11 Then find , (a - 9)2 + 1/((a - 9)^2)

Given = a - \(\frac{1}{a - 9}\) = 11

By subtracting 9 on both sides we get,

(a - 9) - \(\frac{1}{a - 9}\) = 11 - 9 = 2

(a - 9)² + \(\frac{1}{(a - 9)^2}\) = 2² + 2 = 6

 

If x - \(\frac{1}{x}\) = a

then, (x)² + \(\frac{1}{(x)^2}\) = a² + 2