Question

Find two positive real numbers x and y such that their product is 800 and x + 2y is as small as possible.

Answer 1

To find two positive real numbers x and y such that their product is 800 and x + 2y is as small as possible, we can use the concept of minimum and maximum of two variables. There are infinitely many pairs of positive real numbers x and y that satisfy the given conditions.

Step-by-step explanation:

To find two positive real numbers x and y such that their product is 800 and x + 2y is as small as possible, we can use the concept of minimum and maximum of two variables.

1. Let's set up the equation: x * y = 800
2. Since the question states that x + 2y needs to be as small as possible, we can substitute x = 800/y back into the equation to get: (800/y) * y = 800
3. We can simplify this equation to: 800 = 800 which is true for all values of y.

Therefore, there are infinitely many pairs of positive real numbers x and y that satisfy the given conditions.