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![[Post New]](/templates/default/images/icon_minipost_new.gif) 24 Mar 2008 08:22:50 IST
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______________________________________________
Siddhant Shah
The trouble with doing something right the first time is that nobody appreciates how difficult it is.
You can't control the wind, but you can adjust your sails.
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24 Mar 2008 08:38:51 IST
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on multiplying the eqn comes to be--
864x4 - 720x3 + 210x2 - 25x + 1 = 5
on observation / hit and trial 
before getting this equation only we get x = 1/2 , - 1/12 as a solution
dividing the equation by (2x - 1)
we get --
432 x 3 - 144 x 2 + 33 x - 4 = 0
further dividing the equation by (12 x + 1)
we get --
108 x 2 - 45 x + 12 = 0
D = 45 2 - 4*108*12 <=0
hence the given equation has only 2 real roots and 2 imaginary roots
thus it is verified that the answer is 1/2 , - 1/12 and there are not more answers
but this was a method just to verify , i still haven't got a proper method
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Impossible To be Impossible is Impossible |
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Multiply first and last term, 2nd and 3rd term!  This is a quadratic in t. Solve to get  or   or  giving you the solutions  |
Guide to latex:
http://www.goiit.com/posts/list/community-shelf-a-guide-to-latex-48056.htm
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24 Mar 2008 09:09:52 IST
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These type of equations can generally be solved by grouping the terms well. = (12x -1)(3x-1)*(6x-1)(4x-1)=5 implies (36x2 -15x +1)*(24x2 - 10x +1)=5 take 12x2 - 5x =t implies (3t+1)(2t+1)=5 Now you can easily solve for t. That solves the problem! Edit:I didnt see konichiwa2x posted already.
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Destiny is what you make
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24 Mar 2008 09:41:07 IST
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(12x -1).(6x-1).(4x-1).(3x-1) = 5
Multiply both sides by 2 x 3
(12x - 1).(6x - 1).(12x - 3). (6x - 2) = 30
2.(6x - 1/2).(6x - 1). 2.(6x - 3/2). (6x - 2) = 30
(6x - 1/2).(6x - 1).(6x - 3/2). (6x - 2) = 30 / 4
let 6x - 2 = T
T.(T+1/2) (T+1) (T+3/2) = 30 / 4
Also notice 30/4 = 1*2*3*5 / 2*2
= (1) (3/2) (2) (5/2) ---------------------------(1)
OR
= (-1) (-3/2) (-2) (-5/2) ---------------------------(2)
Therefore T = 1 --------------by equating to (1)
or T = -5/2 ----------by equating to (2)
so 6x - 2 = 1
or 6x - 2 = -5/2
So x = 1/2 , -1/12
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---------------------------------------------------------------
- Gaurav Ragtah (spideyunlimited)
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24 Mar 2008 11:57:09 IST
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a tidy little methos frm me..
rite it as (12x-1)(12x-2)(12x-3)(12x-4) = 120
let 12x= y
take y^2 - 5y = z..
put them and solve..
u get z = 16,-6
thus y = 6,-1 & two complex conjugates..
thus x= 1/2 ,-1/12..
just chill..
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Don't Dream ..Do the dream...
Rock On ....
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