If a - 1/(a - 5) = 11 Then find , (a - 5)2 + 1/((a - 5)^2)

Given = a - \(\frac{1}{a - 5}\) = 11

By subtracting 5 on both sides we get,

(a - 5) - \(\frac{1}{a - 5}\) = 11 - 5 = 6

(a - 5)² + \(\frac{1}{(a - 5)^2}\) = 6² + 2 = 38

 

If x - \(\frac{1}{x}\) = a

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