It is known that the sum of two natural numbers is 100. When the two natural numbers are respectively, what is the maximum product of them It's the first day of junior high school It's about the complete square formula hurry up

It is known that the sum of two natural numbers is 100. When the two natural numbers are respectively, what is the maximum product of them It's the first day of junior high school It's about the complete square formula hurry up

Let one number be x, then the other number is 100-x
So the product of two natural numbers m is
M＝X(100－X)
＝－X^2＋100X
＝－(X－50)^2＋2500
Because - (x-50) ^ 2 ≤ 0
So m ≤ 2500
So the maximum value of M is 2500
Here x = 50
That is, when both numbers are equal to 50, their product is the largest, and the maximum value is 2500
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