If x be a natural number, then the number, then the number of possible solutions of the equation ax=

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07 Mar 2013 equaion

If x be a natural number, then the number, then the number of possible solutions of the equation ax=x+6 for various values of a is

OPtion

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

Solution

Given that ax=x+6
therefore x = 6/(a-1)
put a = 2,3,4 and 7
then we have find only 4 solution for value of x is always natural
so answer is 4
option 4

Correct Option: 4 Best Solution (10)

niti   11 years AGO

x=6/(a-1) when a=2,3,4,7 x is a natural number. hence possible number of solution is 4.

Like? Yes (1) | No   

sumit jindal   11 years AGO

x=6/(a-1)
6 have four factors ie. 1, 2 ,3 ,6
these are the four solutions possible..

Like? Yes (4) | No (4)  

dharmendra   11 years AGO

ax=x+6
x(a-1)=6
a!=1
for x to be a natural number
(a-1) should be factor of 6
a-1=1 then x=6
a-1=2 then x=3
a-1=3 then x=2
a-1=6 then x=1

Like? Yes (4) | No (4)  

Mukesh Kr Singh   11 years AGO

since natural no. is 1,2,3,.........upto infinite
so the only value of a=2,3,4,7 we get x as a
which is natural no.

Like? Yes (2) | No (2)  

AVINASH KUMAR   11 years AGO

ax=x+6
x=6/a-1
for x be a natural number.
possible values of a={2,3,4,7}

Like? Yes (2) | No (2)  

Tijo Jose   11 years AGO

ax = x + 6 ==> ax-x = 6
Or, x = 6 / (a-1)
Since x is a natural number, a-1 must be a positive divisor of 6. Since there are four divisors for 6, the answer is 4.

Like? Yes (3) | No (4)  

MONIKA JAIN   11 years AGO

ax=x+6
ax-x=6
x=6/(a-1)
since,x is a natural number,so the possible values of a for which x remains as a natural number are-2,3,4,7.
therefore,total no of solutions of x are=4.
so,answer is 4.

Like? Yes (1) | No (2)  

Vinay Sipani    11 years AGO

ax = x + 6
=> x = 6/(a-1)

=> a = 2,3,4,7
=> 4 solutions possible.

Like? Yes (1) | No (2)  

jitendra singh   11 years AGO

a=2,3,4,7

Like? Yes (1) | No (2)  

phani   11 years AGO

x(a-1)=6====>x can be either 1,2,3,or 6 since x is natural number

Like? Yes (1) | No (3)