What are Two geometric means between 2 and 54?

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Answer 1 · 2018-05-15T17:47:15

# 6, 18#.

We will solve the Question in #RR#.

Let #g_1 and g_2# be the reqd. GMs. btwn. #2 and 54#.

# :. 2, g_1, g_2, 54" must be in GP..."[because," Definition]"#.

#:. g_1/2=g_2/(g_1)=54/(g_2)=r," say"#.

#:. g_1/2=r rArr g_1=2r#,

# g_2/(g_1)=r rArr g_2=rg_1=r*2r=2r^2#,

# 54/(g_2)=r rArr 54=rg_2=r*2r^2=2r^3#.

Now, #2r^3=54 rArr r^3=27 rArr r=3#.

#:. g_1=2r=2*3=6, g_2=2*3^2=18#.

Thus, #6 and 18# are the reqd. (real) GMs.