Question

If the ratio of H.M between two positive numbers "a" and "b" (a>b) is to their G.M as 12 to 13 prove that
a:b is 9:4

Answer 1

@ganeshie8 @DLS

Answer 2

\[\frac{ \frac{ 2ab }{ a+b } }{ \sqrt(ab) }=\frac{ 9 }{4 }\]

Answer 3

It is equal to 12/13

Answer 4

2ab/(a+b)/sqrt(ab) =12/13
or
2sqrt(ab) / (a+b) = 12/13

Answer 5

o yes sorry

Answer 6

after that

Answer 7

or
(a+b)/2sqrt(ab) = 13/12
thus
((a+b) +2sqrt(ab) ) / ((a+b) +2sqrt(ab) ) =(13+12)/(13-12)
or
( sqrt(a) +sqrt(b) )/( sqrt(a) +sqrt(b) ) = 5
or
( sqrt(a) +sqrt(b) ) + ( sqrt(a) - sqrt(b) ) / ( sqrt(a) +sqrt(b) ) - ( sqrt(a) - sqrt(b) ) = (5+1)/(5-1)
sqrt(a/b) =6/4
or a/b =9/4

Answer 8

\[\frac{ 2ab }{ a+b }=\frac{ 12 }{ 13 }\sqrt{ab}\]\[\frac{ 2\sqrt(ab) }{a+b }=\frac{ 12 }{ 13 }\]\[\frac{ \sqrt{ab} }{a+b }=\frac{ 6 }{ 13 }\]

Answer 9

(( sqrt(a) +sqrt(b) ) + ( sqrt(a) - sqrt(b) ) )/ (( sqrt(a) +sqrt(b) ) - ( sqrt(a) - sqrt(b) ) )

Answer 10

how can you write
2ab * sqrt(ab) as 2sqrt(ab)

Answer 11

\[\frac{ a+b }{ \sqrt(ab) }=\frac{ 13 }{ 6 }\]\[\frac{ a }{ \sqrt{ab} }+\frac{ b }{ \sqrt{ab}}\]=13/6

Answer 12

\[\sqrt{\frac{ a }{ b }}+\sqrt{\frac{ b }{ a }}=\frac{ 13 }{ 6 }\]

Answer 13

now let \[t=\sqrt{\frac{ a }{ b }}\]\[t+\frac{ 1 }{ t }=\frac{ 13 }{ 6 }\]

Answer 14

solve for t!!

Answer 15

t= 3 or t= 2/3

Answer 16

t=3/2 and t=2/3

Answer 17

oh yes

Answer 18

\[\sqrt{\frac{ a }{ b }}=3/2\]

Answer 19

a:b=9:4

Answer 20

b:a cannot be 9/4 due to the constraint given that a>b

Answer 21

I have some questions i would tell you in two minutees

Answer 22

I mean questions regarding this question

Answer 23

@No.name
2ab * sqrt(ab) as 2sqrt(ab)
its
2ab/(a+b) / sqrt(ab)/1 = 2ab/ (sqrt(ab)*(a+b))
=2sqrt(ab)/(a+b)

Answer 24

and @No.name i think matricked has applied compenendo and dividendo

Answer 25

yeah