two integers, x and y have a product of 20. what is the least possible sum of x and y?
xy=20
x+y = x + 20/x
minimum occurs where x=2√5
(same as the problem for finding maximum area for a given perimeter: a square)
So, pick two integers near √20. They would be 4 and 5, with sum=9
The only other sums are
1+20=21
2+10=12
To find the least possible sum of x and y, we need to find two integers whose product is 20.
The factors of 20 are (1, 20), (2, 10), and (4, 5).
Out of these pairs, the sum of the two integers is minimized when they are closest to each other.
Thus, the least possible sum of x and y is achieved when x and y are 4 and 5.
Therefore, the least possible sum of x and y is 4 + 5 = 9.
To find the least possible sum of two integers, x and y, with a product of 20, we need to consider all the possible pairs of integers whose product is 20 and then calculate their sums.
First, let's list all the factor pairs of 20:
1 × 20 = 20
2 × 10 = 20
4 × 5 = 20
Now, let's calculate the sums of these factor pairs:
1 + 20 = 21
2 + 10 = 12
4 + 5 = 9
Out of these sums, the smallest one is 9. Therefore, the least possible sum of x and y is 9.