The product of two positive numbers is 1024. What is the minimum value of their sum?

Solution:

Let the first positive number be x.

Let the second positive number be y.

The product of two positive numbers = 1024

x.y = 1024 --- (1)

We have to find the minimum value of the sum.

Sum, S = x + y --- (2)

From (1), y = 1024/x

So, S = x + (1024/x)

Differentiating both sides with respect to x and equating to zero, to find the minimum value of the sum.

dS/dx = 1 - 1024/x² = 0

1 - 1024/x² = 0

1 = 1024/x²

x² = 1024

Taking square root,

x = ±32

Since, the number is positive.

Take x = +32.

Now, y = 1024/32

y = 32

The numbers are 32, 32.

Sum = 32 + 32

Sum = 64

Therefore, the minimum value of their sum is 64.

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The product of two positive numbers is 1024. What is the minimum value of their sum?

Summary:

The product of two positive numbers is 1024. The minimum value of their sum is 64.