Question

If G1 , G2 are two G.M’s between a and b then show that G1G2 = ab.​

Answer 1

Answer:

Step-by-step explanation:

We haveG1 and G2 as two geometric means between b and c i.e.

b,G1,G2,c are in G.P.

c = b {(r)}^{4 - 1} \\ c = {br}^{3} \\

r \: = { (\frac{c}{b} )}^{ \frac{1}{3} }

G1 = br = b.(c/b)^1/3

=> G1^3 = b^3 (c/b) = b^2c

G2 = br^2 = b (c/b)^2/3

=> G2^3 = b^3(c^2/b^2) = bc^2

Hope it helps u