• # question_answer If $a$ be the arithmetic mean of $b$ and $c$ and ${{G}_{1}},\ {{G}_{2}}$ be the two geometric means between them, then $G_{1}^{3}+G_{2}^{3}=$ A) ${{G}_{1}}{{G}_{2}}a$ B) $2{{G}_{1}}{{G}_{2}}a$ C) $3{{G}_{1}}{{G}_{2}}a$ D) None of these

Trick: Put $b=1$ and $c=8$ so that $a=4.5$ and ${{G}_{1}}=2,\ {{G}_{2}}=4$. Now $G_{1}^{3}+G_{2}^{3}=72$. Also option (b) gives this value$i.e.$$2\times 2\times 4\times \frac{9}{2}=72$.