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Question

If A1,A2 be two AM'x and G1,G2 be two GM's between a and b, then find the value of A1+A2G1G2

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Solution

a, A1,A2 b are in A.P.

A1a=A2A1=bA2 ......... (1)

and (a, G1, G2,) b are in G.P.

G1=aG2,G2=G1b

G1G2=sqrtabG1G2

G1G2=ab

G1G2=ab ........... (2)

From equation (1),

2A1=A2+a

2A2=A1+b

Adding these two,

2(A1+A2)=(A1+A2)+a+b

A1+A2=a+b

A1+A2G1G2=a+bab


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