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Algebra

Blazing goIITian

 Joined: 16 Jan 2010 Post: 318
19 Mar 2011 01:43:57 IST
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Please prove these.. If a/b = c/d then prove that, a/b = c/d = (a + c)/(b + d) = root (ac/bd) =
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

Please prove these..If a/b = c/d then prove that,a/b = c/d = (a + c)/(b + d) = root (ac/bd) = (ab + cd)/(b2 + d2)

New kid on the Block

Joined: 19 Mar 2011
Posts: 2
19 Mar 2011 14:23:52 IST
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too basic:, forst is componendo,dividendo on a/c and in next put a=Lb and c=Ld , l belongs to R same in third case

Scorching goIITian

Joined: 2 Mar 2011
Posts: 220
21 Mar 2011 13:51:28 IST
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wuld u pls illustrate

Blazing goIITian

Joined: 1 Jul 2009
Posts: 1416
22 Mar 2011 00:48:11 IST
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All of it can be solved in exactly the same way.

Let a/b=c/d=p

Then, a=bp, c=dp

(a+c)/(b+d) = (bp+dp)/(b+d)=p

rt[ac/bd]=rt[bp*dp/bd]=rt[p²]=p, assuming all of a,b,c,d are +ve nos.

Remember, almost ALL questions in ratio & proprotion and logarithms can be solved in this manner.

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