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Question

If $$G_1$$ and $$G_2$$ are two geometric mean between $$a$$ and $$b$$, then prove that $$G_1 G_2= ab$$.


Solution

Let $$a, G_1, G_2, b$$ are in G.P, 
then $$G_1 = √(aG_2) ....(i)$$ 
Similarly $$G_2 = √(G_1b) ....(ii)$$
Multiplying equation (i) and (ii)
$$G_1\times G_2=\sqrt{G_1G_2}\sqrt{ab}$$
$$\sqrt{G_1G_2}=\sqrt{ab}$$
$$G_1G_2=ab$$


Mathematics

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