If a - 1/(a - 4) = 7 Then find , (a - 4)2 + 1/((a - 4)^2)

Given = a - \(\frac{1}{a - 4}\) = 7

By subtracting 4 on both sides we get,

(a - 4) - \(\frac{1}{a - 4}\) = 7 - 4 = 3

(a - 4)² + \(\frac{1}{(a - 4)^2}\) = 3² + 2 = 11

 

If x - \(\frac{1}{x}\) = a

then, x² + \(\frac{1}{x^2}\) = a² + 2