The sum of a positive number and its reciprocal number (for example x and 1/x) is (2n+1)/6 where n i

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23 May 2012 find number

The sum of a positive number and its reciprocal number (for example x and 1/x) is (2n+1)/6 where n is any integer ranging from 1 to 6. Then the number x will be (out of the 10 options given)

OPtion

1) 1
2) 4
3) 5
4) 8
5) 1/2
6) 3/2
7) 5/2
8) 7/2
9) 7/6
10) none of these

Solution

x + (1/x) = (x^2+1)/x
and we know that x^2+1>2x
so (x^2+1)/x>2
if we take n = 1,2,3,4,5,6 in (2n+1)/6 then for only 6, it will be greater than 2
so definitely n=6
so eq. will become x+(1/x)=13/6
by solving this eq. we will get x = 3/2 and 2/3
but 2/3 is not in the options so answer will be 3/2 out of the 10 given answers

Correct Option: 6 Best Solution (13)

Dr.Dipin Singh   12 years AGO

x+1/x = (2n+1)/6 = 3/6,5/6,7/6,9/6,11/6,13/6

out of these 3/6 and 5/6 are not possible as x+1/x can never be less than 1.
Also
From given options, 1,4,5,8,5/2,7/2 are not possible .

checking 1/2,3/2 and 7/6 , it is found that 3/2 satisfies given condition.
when x=3/2
x+1/x= 3/2 + 2/3 = 13/6 = (2n+1)/6 for n=6

so x= 3/2 .... option 6

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Balakumaran N.A   12 years AGO

x+1/x = (2n+1)/6

when n=6, x+1/x = 13/6... Take x=3/2 from option will satisfy this condition. 3/2+2/3 = 13/6. so, option 6

Like? Yes (2) | No (1)  

Shiv Kumar   12 years AGO

3/2+2/3 = 13/6
For n=6, (2n+1)/6 will be 13/6.

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dileep kumar reddi   12 years AGO

Simple substitution.. and verifying...value of n..

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parul mishra   12 years AGO

option(6)
as n= 1 to 6
now let us assume n=6
from eqn=x+1/x=(2*n+1)/6
x^2+1/x=13/6
on solving we can get x=3/2

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GAURAV KUMAR SRIVASTAV   12 years AGO

because x + 1/x >= 2
so (2n + 1)/6 >=2,
then n >= 5.5

because n is an integer and 1

Like? Yes (2) | No (1)  

Romoni   12 years AGO

if n=1 then 2n+1=3/6
if n=2 then 2n+1=5/6
then it must be 7/6,9/6,11/5,13/6

3/2+2/3=13/6
so option is 6

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Datla Kanthi   12 years AGO

n=6 and x= 3/2 will satisfy the equation in given options

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Karthick Babu   12 years AGO

x+1/x=(2n+1)/6
if n=1,x+1/x=1/2
if n=2,x+1/x=5/6
if n=3,x+1/x=7/6
if n=4,x+1/x=3/2
if n=5,x+1/x=11/6
if n=6,x+1/x=13/6
From the Options, Option (6). x=3/2 gives the result x+1/x=13/6 (that is n=6 result for (2n+1)/6)

Like? Yes (1) | No (1)  

Devendra Marghade   12 years AGO

For x=3/2, x+1/x=3/2+2/3=13/6
We get same value for n=6 in (2n+1)/6

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prithviraj sanningannavar   12 years AGO

for x=3/2 the value of the expression will be 13/6..that is the expression (2n+1)/6 will have n=6

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kalaiarasan   12 years AGO

3/2 + 2/3 =13/6
(2n+1)/6 =13/6
where n=6

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rudrasimhap   12 years AGO

putn=1 to 6 then 6 values out of which only 3/2 is satisfyin..

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