Q4 of 104 Page 477

Insert three geometric means between and 432.

To find: Three geometric Mean


Given: The numbers and 432


Formula used: (i) r , where n is the number of


geometric mean


Let G1, G2 and G3 be the three geometric mean


Then r


⇒ r


⇒ r


⇒ r


⇒ r


⇒ r = 6


G1 = ar = ×6 = 2


G2 = ar2= ×62 = ×36 = 12


G3 = ar3= ×63 = ×216 = 72


Three geometric mean between and 432 are 2, 12 and 72.


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2

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(ii) 1 and


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(vi) ad ab3


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The AM between two positive numbers a and b(a>b) is twice their GM. Prove that a:b .