Question

Find two geometric means between 4 and 13.5

Answer 1

two geometric means between 4, 13.5 are 6 and 9

Answer 2

so r1/4 = 13.5/r2 = r2/r1

r1*r2 = 54 ----------eqn(1)

r2^2 = 13.5r1--------eqn(2)

from(2) r1 = r2^2/13.5

substituting this in eqn(1)

r2^3/13.5 = 54

r2^3 = 54*13.5 = 729

r2 = 9

r1 = 81/13.5 = 6

so two geometric means between 4, 13.5 are 6 and 9