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

Given = a - \(\frac{1}{a - 1}\) = 7

By subtracting 1 on both sides we get,

(a - 1) - \(\frac{1}{a - 1}\) = 7 - 1 = 6

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

 

If x - \(\frac{1}{x}\) = a

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