Among all pairs of numbers with a sum of 149149, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Correct question is;

Among all pairs of numbers with a sum of 149, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms

The pair whose product is maximum is 149/2 and 149/2

Step-by-step explanation:

We are told that pair of number with sum as 149 and to find the product that is maximum.

Now,let x and y be the numbers. Thus;

x + y = 149 and xy is maximum.

So, y = 149 - x

Thus, plugging 149 - x for y into the product equation gives; x(149 - x). This can be expanded to be -x² + 149x.

Using method of completing the square, we will arrive at;

-(x² - 149x) = -(x² -149x + (149/2)²) + (149/2)² = (149/2)² - (x - (149/2))²

Now, the expression gotten will have a maximum of (149/2)² when (x - (149/2))² has its minimum value of zero. This means that when x = 149/2, as x moves away from 149/2, (149/2)² would be reduced by the square of the difference between the value of x and 149/2, and the square would always be positive.

Thus, the maximum product in it's simplest form is x = y = 149/2

step-by-step explanation: