Question

A Positive number & its reciprocal are said
to be:
​

Answer 1

Answer:

A Positive number & its reciprocal are said

to be Inverse Propotion

Answer 2

Step-by-step explanation:

Let x be the number, so 1x is its reciprocal. The sum, S , is given by:

S=x+1x

S=(xx)x1+1x=x2x+1x=x2+1x

Now we want to find the minimum value of S, so we’ll take the derivative of S with respect to x:

dSdx=1−1x2

Now set the derivative equal to zero, because we want to find the extrema:

1−1x2=0

−1x2=−1

1x2=1

x2=1

x=±1

We can discard the negative solution, since you specified that the number is positive.

x=1

And the smallest possible sum is:

S=1+1(1)=2