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Cool goIITian

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26 Mar 2009 16:35:14 IST

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solve 4[x] = x + {x} , where {.} is fractional part of x and [x] is greatest integer function.

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solve 4[x] = x + {x} , where {.} is fractional part of x and [x] is greatest integer function.

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saharsha kumar keshkar

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26 Mar 2009 16:45:30 IST

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4[x]=[x]+{x}+{x}

3[x]=2{x}

as we know that...

0<={x}<1

0<=2{x}<2

substitute...

0<=3[x]<2

0<=[x]<2/3

hence....[x] only value of 0.

now sbstitute..in main eqn...

4[x]=x+(x-[x])..

getting value x =0....

nudge me if i m wrong...

$hivani Gupta ¤

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26 Mar 2009 16:48:13 IST

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is d ans 0<= x <= 5/3

try by writing

then we get x=5/3

as fractional part lies b/w 0 nd 1 so we get tht ans

saharsha kumar keshkar

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26 Mar 2009 16:49:33 IST

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shivani i think u r wrong............

$hivani Gupta ¤

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26 Mar 2009 16:55:29 IST

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i hav seen again cant see d fault plz u tell.

n s.bharthwaj plz tell d correct ans

$hivani Gupta ¤

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26 Mar 2009 16:55:41 IST

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i hav seen again cant see d fault plz u tell.

n s.bharthwaj plz tell d correct ans

saharsha kumar keshkar

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26 Mar 2009 17:06:11 IST

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shivani i think....

u mistook th question as..4{x}=x+[x]

but the question is different...

nudge me if i m wrong...

srinija

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26 Mar 2009 17:07:46 IST

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evn i think the ans is zero.ya we get x=5/3{x} and x=5/2[x] also [x]=2/3{x}for [x] to b defined {x} should be of 3n(n E I) type or 3/2 since both r not true ..we can conclude that zero is the only posbl sol...

saharsha kumar keshkar

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26 Mar 2009 17:16:16 IST

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shivani is also correct.........

4(x-{x})=x+{x}

3x=5{x}.......

but................................

srinija

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26 Mar 2009 17:29:48 IST

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0<= x <= 5/3

is shivani's ans..chk the boundry condition.

if x=5/3 then the eqn is not satisfied.

so x=o seems more correct

rakesh bokaro

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26 Mar 2009 17:31:58 IST

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so which is correct.....saharsha's solution is correct....

AIR 538 Asish

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26 Mar 2009 17:41:05 IST

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yup saharsha is correct... in shivani's solution the initial condition is ok.. but u have to find the value of x that satisfies the original equation i.e. solving we get x=0

ar rehman

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26 Mar 2009 17:43:17 IST

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thanks for confirming abt answer....

Giving An Ax

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26 Mar 2009 18:47:37 IST

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THanks guys for the answer. and the ans is of course 0.

Giving An Ax

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26 Mar 2009 18:49:57 IST

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saharsha's ans is perfect.One more question and please check it under diff. calculus.

$hivani Gupta ¤

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26 Mar 2009 22:32:59 IST

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yup rite got it frnds thnx for correcting

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