Algebra

Blazing goIITian

Joined: 2 Aug 2010
Post: 366
9 Aug 2010 00:31:51 IST
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do it , if alpha beta gama are the rootsof x^3-x-1=0 then 1+alpha/1-alpha+1+beta/1
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

do it , if alpha beta gama are the rootsof x^3-x-1=0 then 1+alpha/1-alpha+1+beta/1-beta+1+gama/1-gama=



Comments (6)


New kid on the Block

Joined: 18 Jul 2010
Posts: 7
12 Aug 2010 06:22:44 IST
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answer is very simple.answer=-1/3

New kid on the Block

Joined: 9 Aug 2010
Posts: 3
13 Aug 2010 00:42:29 IST
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just simplyfy the whole thing and use the summation and products of roots........As simple as it seems to be.....

Blazing goIITian

Joined: 16 Jan 2010
Posts: 318
14 Aug 2010 11:37:01 IST
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Someone please solve!!!!!!!!!!!!!!!!!!!!!!

Blazing goIITian

Joined: 16 Jan 2010
Posts: 318
14 Aug 2010 11:41:48 IST
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clearly, alpha + beta + gama = 0 ------ (i)

alpha2 + beta2 + gama2 = -1

alpha x beta + beta x gama + gama x alpha = -1

alpha x beta x gama = 1
So,on dividing alpha x beta + beta x gama + gama x alpha by alpha x beta x gama we get,

1/alpha + 1/beta + 1/gama = -1

Adding 3 to both the sides we get

(1 + alpha)/alpha + (1 + beta)/beta + (1 + gama)/gama = 2

But what next to do??????????

Cool goIITian

Joined: 30 May 2010
Posts: 48
15 Aug 2010 13:31:44 IST
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 use trasformation of eqns read bs grewal for details

Hari Shankar's Avatar

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Joined: 28 Feb 2007
Posts: 2217
17 Aug 2010 16:50:49 IST
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