If 1/((x-2)) + x = 8 , then what is the value of 1/((x-2)^2)+(x - 2)^…

If $K+\frac{1}{K}=n$

then, $K^2+\frac{1}{K^2}$ = n² – 2

If $\frac{1}{(x-2)} + x = 8 $,

then what is the value of $\frac{1}{(x-2)^2}+(x - 2)^2 $ ?

Subtract 2 from both the sides,

$\frac{1}{(x-2)} + (x-2) = 8-2 $,

$\frac{1}{(x-2)} + (x-2) = 6 $,

$\frac{1}{(x-2)^2}+(x - 2)^2 $ = 6² – 2 = 34