If one root of the equation $4{\mathrm{x}}^2-2\mathrm{x}+\mathrm{k}-4=0$ is the reciprocal of the other, then the value of k is

$4{\mathrm{x}}^2-2\mathrm{x}+\mathrm{k}-4=0$

One root is $\alpha$ then other root is $\frac{1}{\alpha }$ so,

Product of the roots is $\frac{c}{a}$ then

$\Rightarrow a\times \frac{1}{a}=1$

$\frac{k-4}{4}=1$

$k=8$