If $a+(1/(a-2))=4 $ then $(a-2)^2+(1/(a-2))^2$ is .

Question

If $a+(1/(a-2))=4 $ then $(a-2)^2+(1/(a-2))^2$ is .

Note: $a^2+(1/(a-2))^2=4^2$

Answer 1

Hint

Remark that $$(a-2)^2+\frac{1}{(a-2)^2}=\Big((a-2)+\frac{1}{(a-2)}\Big)^2-2$$

I am sure that you can take from here.

Answer 2

Let $u = a-2 $
$$u+2 + \dfrac{1}{u} = 4 \implies u + \dfrac{1}{u} = 2 $$

square both sides