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Algebra
pasu shah
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Joined: 5 May 2009
Post: 57
7 Jan 2011 22:18:17 IST
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Find solution:(x)[x]=1. here ( ) is Least Integer Function. [ ]=Greatest Integer Function
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

Find solution:(x)[x]=1. here ( ) is Least Integer Function.[ ]=Greatest Integer Function


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arna ghosh
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Joined: 8 Dec 2010
Posts: 85
8 Jan 2011 18:39:42 IST
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since both (x) and [x] are integers and their product is 1, the have to be both 1 or (-1).

CASE I   (x)=[x]=1

  (x) = [x] only if x is an integer.

so here x = 1.

CASE II    (x)=[x]= (-1)

Similarly, here x = (-1)

thus, there are 2 solutions :- 1 and (-1)
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SUHAG SIR , Bhopal's Avatar

SUHAG SIR , Bhopal
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Joined: 5 Jan 2011
Posts: 116
8 Jan 2011 21:20:03 IST
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Here arna ghosh is correct with very good explination there are two ans. 1 and -1. www.tekoclasses.com
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