# Maximum value of (x*y) if (x+y) is given

Can anyone give me the solution?

Can anyone help me to solve this problem. please

You can think like if the product of number should be largest and one number is negative, the product should be close to 0 only. So like in the image you shared if 2=X+Y, then X and Y can be {(3,-1), (4,-2), (5,-3), etc…}. So as we can se by multiplying that largest number out of {(-3,-8,-15, etc…} is -3. when multiplied by -1. Similarly in next example 0, it can be done by (1,-1). Hope you got this.

I want the logic to solve this problem. can you write it ?

I have already given the logic. What do you mean?
It will be (x+1)*-1

since you want minimum value of x*y
and y is negative so it should be close to 0 so take value of y as -1 and remaining as x
test case 2 ,y =-1 and x=3
0, y=-1 and x=1

take y=-1 as we have to take y as negative, to make the max value of p we need to take the least negative value of y which is y=-1.

Guys, can you please write the code here?
I am not able to solve.
If you give me the code, I will try to understand.

Can you please write the code here?
I am not able to solve.

We can apply the idea of quadratic equations to determine the greatest value of the product (x * y) when the total (x + y) is given.

Assume that (x + y) is equal to C, which is a constant value. Thus, we have the following equation:

x + y = C

Rearranging the equation will allow us to solve for one variable in terms of the other:

x = C - y

This expression may now be used to calculate the product (x * y) of x and y:

P = (C - y) * y

Extending the formula:

P = C*y - y^2

We can take the derivative of P with respect to y and set it to zero to get the highest value of P:

C - 2y = dP/dy = 0

calculating y:

0 2y = C, 2y = C, and y = C/2

Now that we have the value of y, we can substitute it back into the equation x + y = C to find x:

x + C/2 = C
x = C - C/2
x = C/2

So, the maximum value of the product (x * y) occurs when x = C/2 and y = C/2.

Therefore, the maximum value of (x * y) is (C/2) * (C/2) = C^2 / 4.