If $\lambda \ne \mu$ and ${\lambda }^2=5\lambda -3,{\mu }^2=5\mu -3$ , then the equation whose roots are $\frac{\lambda }{\mu }$ and $\frac{\mu }{\lambda }$ is

${\mu }^2=5\mu -\Rightarrow {\mu }^2-5\mu +3=0$

$\therefore \lambda ,\mu$  are roots of $x^2-5x+3=0$

$\therefore \lambda +\mu =5,\lambda \mu =3$

Then quadratic equation whose roots are

$\frac{\lambda }{\mu }\&\frac{\mu }{\lambda }$ is $x^2-x\left(\frac{{\lambda }^2+{\mu }^2}{\lambda \mu }\right)+1=0$

$\Rightarrow 3x^2-19x+3=0$