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If A1 and A2 be two AM 's and G1 and G2 be GM 's between 'a' and 'b', then find the value of (A1+A2) / ( G1*G2 ) !! thanks in advance !

If A1 and A2 be two AM 's and G1 and G2 be GM 's between 'a' and 'b', then find the value of (A1+A2) / ( G1*G2 ) !!


thanks in advance !

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

A1 , A2 are inserted bw a,b ...

total terms now are 4 ...

let common difference is d then

a+(n-1)d = b

a+(4-1)d = b

3d = b-a .................1

second term is A1 = a+d

third term is A2 = a+2d

A1+A2  = 2a+3d = 2a+b-a                        (by using 1)

                       =a+b

now if A1,A2 are Gm's bw a,b then

 arn-1 = b

 ar3 = b

  r3 = b/a    ............2

2nd term is A1 = ar

third term is A2 = ar2

A1A2 = a2r3 = ab              (by using 2)

now A1+A2/A1A2 = a+b/ab

approve if u like my ans

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