How do you find two numbers whose product is given?

If you are asked to work out the product of two or more numbers, then you need to multiply the numbers together. If you are asked to find the sum of two or more numbers, then you need to add the numbers together.

How do you find the two positive real numbers whose sum is 40 and whose product is a maximum?

1 Answer

1. The problem states that we are looking for two numbers x and y such as x+y=40 , that is.
2. y=40−x.
3. We would like to find where the product x⋅y is maximum, but from the above equation we can write:
4. x⋅y=x⋅(40−x)=−x2+40x .

What does it mean when the product of the numbers is negative and positive?

The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.

What does it mean when the product of the numbers is negative or positive?

When multiplying numbers, the magnitude of the product is always just the product of the two magnitudes. The sign of the product is determined by the following rules: The product of one positive number and one negative number is negative. The product of two negative numbers is positive.

What are two positive numbers whose sum is 100 has the largest product?

Rearrange the constraint to y = 100 – x, and substitute into the product equation. Differentiate again to check that this is indeed a maximum. The second derivative is always negative so A = 100x – x2 is always concave so the critical point is indeed a maximum. So the answer is x = 50 and y = 50.

What are the two positive real numbers with sum of 26 and a product that is as great as possible?

Originally Answered: What are the two positive real numbers with a sum of 26 and a product as great as possible? Product of two numbers is greatest when they are equal. So if their sum is 26, the two numbers should be 13 each for the product to be maximum which is 169. The two positive real numbers are 13 & 13.

What is the maximum product of two numbers having a sum of 50?

What are two numbers with the sum of 50 a product that is as great as possible? – Quora. f(x) = x (50 – x) = 50 x – x^{2}. x=y=25. So, the maximum of the product is 625 and occurs when the numbers are of equal value, which is 25.

What is the sum of two positive numbers?

always positive
The sum of two positive integers is always positive.

Why do 2 negatives make a positive?

Each number has an “additive inverse” associated to it (a sort of “opposite” number), which when added to the original number gives zero. The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.

What is the product of two positive numbers?

RULE 2: The product of two positive integers is positive.