Question

insert 4 geometric means between 3 and 96.Also show the product is the 4 th power of G. M. between them​

Answer 1

Let G1, G2, G3, G4 be the required geometric means. Then, 3, G1, G2, G3, G4, 96 are in G.P. Let r be the common ratio. Here 96 is the 6th

. . . 96 = ar^6-1 = 3r

r^5 = 32 = (2)^5

r = 2

. . . G1 = ar = 3 × 2 = 6,

G2 = ar^2 = 3 × 2^2 = 12

G3 = ar^3 = 3 × 2^3 = 24

G4 = ar^4 = 3 × 2^4 = 48

Also, if G is the G.M. between 3 and 96,

then G = √3×96 = √288 = 12√2

Now G1 × G2 × G3 × G4 = 6× 12× 24× 48

= 12^42^2

= ( 12√2)^4

4th power of G.M. between 3 and 96

hope it will help you ☺️

Answer 2

Answer:

The answer is provided in the above picture