Question

Please see attachment

Answer 1

@amistre64 @satellite73 @Callisto

Answer 2

is that really algebra?

Answer 3

topic is ratio and proportion and i include this in algebra though may be deeper in algebra section

Answer 4

(a:b) = (c:d) is given
(e:f) = (g:h) is given

prove: (ae+bf):(ae-bf) = (cg+dh):(cg-dh)

since ratios are fractions, we can rewrite these as fractions

a/b = c/d
e/f = g/h

\[\frac ab + \frac ef = \frac{af+be}{bf}\]
\[\frac cd + \frac gh = \frac{ch+gd}{dh}\]

since like parts added to like parts are equal

\[\frac{af+be}{bf} = \frac{ch+gd}{dh}\]
got no idea if this thought is even in the right track :)

Answer 5

i will try to do something more about this and post my answer till tomorrow .. @amistre64
thanks though

Answer 6

working backwards i get; so reversing it should get you there\[\frac{(ae+bf)}{(ae-bf)} = \frac{(cg+dh)}{(cg-dh)}\]
\[(ae+bf)(cg-dh) = (cg+dh)(ae-bf)\]
\[aecg-aedh+bfcg-bfdh = cgae-cgbf+dhae-dhbf\]
\[-aedh+bfcg = -bfcg+aedh\]
\[2bfcg = 2aedh\]
\[1=\frac{aedh}{bfcg}\]\[\frac{bc}{eh}=\frac{ad}{fg}\]
\[ad=bc;\ eh=fg\]
\[a:b=c:d;\ e:f=g:H\]

Answer 7

So coming to the question again @amistre64 ::

You are getting answer by reverse method , right? but not able to prove that

Can you think of any other method please?

Answer 8

m i right @amistre64 and @TuringTest

Answer 9

the reverse method establishes a viable path way since there are numerous routes to take and we are looking for a specific one. also, i never know how much reinventing of the wheel has to take place to qualify as a proof in these things :/

Answer 10

hmn ... i agree but the answer given by me . are the steps right? any mistake there