If m + 1m - 2 = 4 , find the value of ( m - 2 )^2 + 1 ( m - 2 )^2 is?

Answer: Option C

$$\begin{array}{rl}& m+\frac{1}{m-2}=4\\ & \Rightarrow m-2+\frac{1}{m-2}=2\\ & \left(\text{Squaring the both sides}\right)\end{array}$$
$$\Rightarrow {\left(m-2\right)}^2\text{ + }\frac{1}{{\left(m-2\right)}^2}+2\times$$      $$\left(m-2\right)\times$$  $$\frac{1}{\left(m-2\right)}$$   $$=4$$
$$\Rightarrow {\left(m-2\right)}^2\text{ + }\frac{1}{{\left(m-2\right)}^2}=2$$