Let's do some more practice of this concept.
All right, say X and Y is given us ninety six and you need to maximize X plus.
So what would be the case?
What are all the possibilities in which I can write X and Y is ninety six.
All right, these are all my possibilities.
I can have one in the ninety six point forty three PRENDA thirty two or twenty four.
I don't have five into something because I went to ninety six by five would give me ninety six, but
nine to six by five is not an integer.
All right, so over here we are taking the Kasmir X and Y has to be integers.
All right.
Now what about six.
The 16.
That's also nine, six, seven and two.
Ninety six by seven is a ninety six.
Ninety six by seven is not an integer.
So we are not taking it and we have eight to 12.
Now the next one after this would be well we do it right.
So that's a repetition of this one.
We don't take it and we stop at this point.
Now in which case will X plus why be the maximum.
Right.
That's what we have to do.
So you will find that when X and Y are kept as far apart as possible, you will get the maximum X plus.
So that is over here.
That's one plus ninety six, which is ninety seven.
Now when would it be minimum.
It would be minimum when you keep it as close as possible.
Right.
So that would be this case.
That is eight plus twelve is equal to twenty.
Now let's do one more example.
Say X plus why he's given us twenty four and X and Y as to be integers.
And you need to maximize the product and minimize the product to try it on your own before we do it
together.
All right, let's do it together.
What are all the possibilities were?
Plus, why is equal to twenty four.
It can be one plus twenty three, two plus twenty two, three plus twenty one etc. up to twelve plus
twelve.
Right.
Because beyond that, what would be the next one.
It will be thirteen plus eleven.
Right.
And you will see that that's what would have been covered already.
Here you have eleven over here and thirteen over here.
So it's a repetition.
So we stop at twelve, twelve right now.
Among all of these when will X in Dubai be maximum.
It will be maximum when you keep X and Y as close as possible.
That would be over here.
12 and 12 are the same number.
So they are very close to each other.
There is no distance between them.
So twelve in the twelve is one forty four and that is the maximum X into right now.
If you want to minimize, you need to keep X and Y as far apart as possible.
But that's one in the twenty three which gives you twenty three.