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Algebra

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 Joined: 19 Feb 2007 Post: 3836
30 Mar 2007 20:10:54 IST
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16
6046
AP GP HP is nt difficult
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

important pts.

1) If Tp = P , Tq = Q in a GP then , T= { Pn - q / Q n - p }1 / p - q

2)  Tm + n = P  , Tm - n = Q in a GP then Tm = PQ   ,  Tn = p  (q/p)m/2n

3) Tm = n        Tn = m in a HP then Tm + n = mn / m + n

4) Tp = qr        Tq = pr in a HP  then tr = pq

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30 Mar 2007 20:20:10 IST
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A , G , M  are the AM ,  GM ,  HM b/w a and b then

an + 1 + bn + 1 / an + bn = A when n=0

an + 1 + bn + 1 / an + bn = B when n = -1/2

an + 1 + bn + 1 / an + bn = C when n = -1

-------> If
a - b / b - c
= 1 (abc are in AP)
= a/b (abc are in GP)
= a/c(abc are in HP)

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Joined: 19 Feb 2007
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30 Mar 2007 21:02:13 IST
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--->In an AP , if a is the 1st term , d is the common diff. , having m terms then nth term frm end is a + (m - n )d
--->Relation b/w AM GM HM
A > G > H and  AGH are in GP  G2 = AH
---> If pth term of an AP is q and qth term is p then
Tp+q = 0
Tr = p + q - r
---> pTp = qTq of an AP then
T P+q = 0

Blazing goIITian

Joined: 9 Feb 2007
Posts: 1347
30 Mar 2007 23:15:57 IST
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superb yaar !!! gr8 !!!!!

Blazing goIITian

Joined: 12 Nov 2006
Posts: 413
30 Mar 2007 23:36:08 IST
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some more..........

if for a G.P, Tp=p,TQ=q,   Tn=[pn-Q/qn-p]1/p-q

If for a G.P Tm+n=p, Tm-n =q thenTm=sqr rt(pq), Tn=p(q/p)m/2n

==>if a,b,c, are the pth,qth,rth terms of a G.P then aq-r.br-p.cp-q=1

==> an+1+bn+1/an+bn is G.M betwen a and b if n=1/2

thank u!!!!!!!!

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Joined: 19 Feb 2007
Posts: 3836
31 Mar 2007 12:09:54 IST
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good one arjun!!!!!!!!!!!!!

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Joined: 6 Jan 2007
Posts: 706
31 Mar 2007 13:21:43 IST
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Here are some more!
If A and G be the AM and GM between two numbers a,b then a,b are given by
A (A+G)(A-G)

If H is the HM between a and b then,
(H-2a)(H-2b)=H2
(1/(H-a))+(1/(H-b))=(1/a)+(1/b)
((H+a)/(H-a))+((H+b)/(H-b))=2

If a,b,c are any numbers then,
a3+b3+c3-3abc=(a+b+c)(a+bw+cw2)(a+bw2+cw)
where w is cube root of unity.

Forum Expert
Joined: 19 Feb 2007
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31 Mar 2007 22:04:10 IST
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great one
cool

New kid on the Block

Joined: 12 Apr 2007
Posts: 21
23 Apr 2007 15:25:03 IST
1 people liked this

good......

Forum Expert
Joined: 19 Feb 2007
Posts: 3836
19 May 2007 19:32:44 IST
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thanx fr the rates :))

Blazing goIITian

Joined: 21 Apr 2007
Posts: 485
25 Aug 2007 00:49:50 IST
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awesome................xtremely .useful.........

thanx.....

keep it up.......

New kid on the Block

Joined: 3 Apr 2007
Posts: 29
2 Sep 2007 14:27:48 IST
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thanx u r the best yaarrrrrrrrrrrrrr

Hot goIITian

Joined: 8 Jan 2008
Posts: 188
27 Jan 2008 20:59:52 IST
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awesum yaar

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Joined: 19 Feb 2007
Posts: 3836
27 Jan 2008 22:15:09 IST
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Thanq :)

Blazing goIITian

Joined: 27 Dec 2007
Posts: 822
12 May 2008 02:20:18 IST
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one more for objective approach:

2,3,6 are three numbers in HP

3,4,6,12 are four numbers in HP

juz put the values n get the answer..

New kid on the Block

Joined: 8 Feb 2009
Posts: 1
15 Feb 2009 22:00:56 IST
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hey,svj..ur trick wz awesum..

thnx..

Cool goIITian

Joined: 15 Apr 2008
Posts: 96
28 Mar 2009 22:10:58 IST
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thnk ya..

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