In the space below, provide the larger of the positive integers that add to 10 and have the largest possible product
larger number x
smaller number 10-x
product = xy = x(10-x)
(I predict using common sense that the two numbers will be 5 and 5)
P = 10x - x^2
this is a downwards parabola, and it will have a max at its vertex
the x of the vertex is -b/(2a) = -10/-2 = 5 , (see, I told you)
so the two numbers with the largest product (25) and a sum of 10 are 5 and 5
Since neither number is larger than the other, the phrasing of the question is bogus.
To find the larger positive integers that add to 10 and have the largest possible product, we can use a simple mathematical approach.
Let's assume the two positive integers as x and y. According to the problem, we know that x + y = 10.
To find the largest possible product, we need to find values for x and y that make their product as large as possible. The product of two numbers is maximum when they are as close to each other as possible.
To find the largest possible product, we can consider both x and y as 5 each. In this case, the sum of the two numbers would be 5 + 5 = 10, which satisfies the condition.
The product of two numbers x and y would be:
Product = x * y = 5 * 5 = 25
Therefore, the larger of the positive integers that add to 10 and have the largest possible product is 5.