What positive number added to its reciprocal gives the minimum sum?

Answer 1

Let x be the positive number we're looking for.

The sum of x and its reciprocal is:

x + 1/x

We want to find the value of x that minimizes this sum.

One way to do this is to use calculus. We can take the derivative of the sum with respect to x, set it equal to zero to find the critical points, and then test those points to see which one gives the minimum value.

The derivative of the sum is:

1 - 1/x^2

Setting this equal to zero and solving for x, we get:

x^2 = 1

x = 1 or x = -1 (but we discard this solution since we are looking for a positive number)

So, the minimum sum occurs when x = 1.

Checking, we have:

1 + 1/1 = 2

This is the minimum possible value of the sum. Therefore, the positive number we're looking for is 1.