im stuck in this question,i tried everything but i failed... can u please help me.

find two numbers whose sum is 32 and whose product is a maximum.

please help me!!!

why don't you make 3 columns,

first one x, second one y, third one xy
then

2 30 60
3 29 87
4 28 112
.
.

until xy, or the product, becomes as large as possible.

Of course, I'm here to help you. Let's break down the problem and find a solution step by step.

To find two numbers whose sum is 32 and whose product is maximum, we'll use algebraic reasoning. Let's call the two numbers x and y.

1. The sum of the two numbers is 32. Writing this as an equation, we have:
x + y = 32

2. The product of the two numbers is what we want to maximize. Writing this as an equation, we have:
xy = ?

To find the maximum value of the product, we can make use of the AM-GM inequality. According to this inequality, the arithmetic mean (AM) of two positive numbers is always greater than or equal to the geometric mean (GM) of those numbers. Mathematically, it can be written as:

(x + y) / 2 ≥ √(xy)

This inequality tells us that the sum of the two numbers divided by 2 must be greater than or equal to the square root of their product.

3. Rearranging the inequality, we have:
x + y ≥ 2√(xy)

4. Now, let's substitute the sum value (32) into our inequality:
32 ≥ 2√(xy)

5. Simplifying the inequality, we have:
16 ≥ √(xy)

6. Squaring both sides of the inequality to remove the square root, we obtain:
256 ≥ xy

From here, we see that the maximum value for the product xy is 256. The equality is achieved when x = y = 16. Therefore, the two numbers whose sum is 32 and whose product is a maximum are both 16.

So, the answer to your question is that the two numbers are 16 and 16.