Question

Two positive numbers x and y, with the maximum value 4, add up to 5. what is the difference between the maximum and minimum value of the product x^2y^3.

Answer 1

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,

$x\leq 4,y\leq 4$      ....(i)

So,

$x^2y^3\leq 4^2 4^3=1024$

So, maximum value of the product $x^2y^3$ is 1024.

Also, its given that sum of numbers x and y is 5, so $x+y=5$   ...(ii)

On using equations (i) and (ii), we get

$1\leq x,1\leq y$

So,

$1\leq x^2y^3$

Therefore, minimum value of the product is 1.

Difference between the maximum and minimum value of the product =  maximum value of the product $x^2y^3$ - minimum value of the product

=1024 - 1 = 1023