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Find largest integer x for which another integer n exists with nx = n + 12x

Find largest integer x for which another integer n exists with      nx = n + 12x

Grade:12th

4 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Abhishek,

 

Rearrange the given equation, and we have:

x(n-12) = n

Or x = n/(n-12).

Now we have to find the largest x --------- (So we will assume x to be positive, since if it is negative, then it cannot be the largest).

 

So x = n/(n-12).

So we have to maximise n/(n-12).

 

Now, x = n/(n-12) = 1 + 12/(n-12).

This will clearly be maximum when (n-12) = 1..... ie n = 13.

 

So the maximum value of x will be 13.

 

Hope this helps.

Wish you all the best.

 

Regards,

Ashwin (IIT Madras).

Sathya
35 Points
9 years ago

I thought the maximum value for it will be 12 because:

 

As  x = n/(n-12)

When n=12, x=12/0=Infinity.......

Thus it should be 12 na?

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Satyaram,

 

No n cant be 12.

Put n=12 in the original eqn,

You will get 12x = 12+12x....

Which is absurd.

 

Hence x = 13, fon n=13.

 

Regards,

Ashwin (IIT MadraS).

Sathya
35 Points
9 years ago

But wats wrong in it dude?

 

 nx = n + 12x

 

 

Or x = n/(n-12)

 

Substitute n=12,

12/12-12=12/0 = Infinity=x....

 

Substitute n=13,

13/13-12=13/1=13=x

 

Since Infinity is greater than 13,

Y,The Largest value for x should not be 13?......

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