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Question

Find the geometric means of the following pairs of numbers:
(i) 2 and 8
(ii) a3b and ab3
(iii) −8 and −2

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Solution

(i) Let the G.M. between 2 and 8 be G.Then, 2, G and 8 are in G.P. G2=2×8G2=16G=±16G=±4

(ii) Let the G.M. between a3b and ab3 be G.Then, a3b, G and ab3 are in G.P. G2=a3b×ab3G2=a4b4G=a4b4G=a2b2

(iii) Let the G.M. between -8 and -2 be G.Then, -8, G and -2 are in G.P. G2=-8-2G2=16G=±16G=4, -4

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