Answer:
1023
Step-by-step explanation:
Positive numbers are numbers that are greater than 0.
As maximum value of numbers x and y is 4,
....(i)
So,
![x^2y^3\leq 4^2 4^3=1024](https://tex.z-dn.net/?f=x%5E2y%5E3%5Cleq%204%5E2%204%5E3%3D1024)
So, maximum value of the product
is 1024.
Also, its given that sum of numbers x and y is 5, so
...(ii)
On using equations (i) and (ii), we get
![1\leq x,1\leq y](https://tex.z-dn.net/?f=1%5Cleq%20x%2C1%5Cleq%20y)
So,
![1\leq x^2y^3](https://tex.z-dn.net/?f=1%5Cleq%20x%5E2y%5E3)
Therefore, minimum value of the product is 1.
Difference between the maximum and minimum value of the product = maximum value of the product
- minimum value of the product
=1024 - 1 = 1023