Explanation:
\({L_S} = {L_1} + {L_2} = 10\,H\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
\({L_P} = \frac{{{L_1}{L_2}}}{{{L_1} + {L_2}}} = 2.4\,H\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
On solving (1) and (2) \({L_1}{L_2} = 24\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)\)
Also \(\left(L_{1}-L_{2}\right)^{2}=\left(L_{1}+L_{2}\right)^{2}-4 L_{1} L_{2}\)
\(\Rightarrow\left(L_{1}-L_{2}\right)^{2}=(10)^{2}-4 \times 24=4 \Rightarrow L_{1}-L_{2}=2 H\)