Question

The A.M between two number is 40. And their H.m is 30.find the number

Answer 1

Answer:

Let the numbers be a, b and their A.M., G.M., and H.M. be denoted by

A,G, and H respectively. Also we know that A.G.H are in G.P.

or G 2

=AH ...(1)

Since A−G=15 and A−H=27(A−15) 2

=G 2

=AH by (1) =A(A-27)

or −30A+225=−27Aor3A=225

∴A=75

= 2a+b

∴a+b=150 ...(2)

Since A−G=15∴75−G=15or G=60

= abab

=3600...(3)

Hence from (2) and (3) we conclude that a and b are the roots of t 2−150t+3600=0or (t−120)(t−30)=0∴t=120,30

Hence the two numbers are 120 and 30.