Question

What is the least possible sum of a positive number and its reciprocal is?

Answer 1

Let this number be x. Then its reciprocal is 1/x. And the sum of them is x+1/x.

In order to find the least possible sum, we can derivate the sum and set it to zero.

Derivation of x+1/x gives us,
`1- x^(-2)`. Setting it to zero, we are going to solve the following equation:
`1- (1)/( x^(2) ) =0`

And solving it, we obtain x=1 and x=-1. Since we were looking for a positive number, the answer is 1