Question

If the average of a number N and its reciprocal is 1, what is the number N?

Answer 1

(n + 1/n)/2 = 1

n^2 + 1 = 2n
now solve in the usual ways

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the number N, we need to set up an equation based on the given information.

Let's assume the number N is N.

The average of a number N and its reciprocal is 1 can be expressed as:

(N + 1/N) / 2 = 1

To simplify the equation, we can multiply both sides by 2:

N + 1/N = 2

Next, we can multiply both sides by N to eliminate the fraction:

N^2 + 1 = 2N

Rearranging the equation:

N^2 - 2N + 1 = 0

This is a quadratic equation, and it can be factored as:

(N - 1)(N - 1) = 0

So, N - 1 = 0

Therefore, N = 1.

Hence, the number N is 1.

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem, we need to translate the given information into a mathematical equation and then solve for the unknown variable, N.

Let's start by writing down the equation based on the given information:

Average of N and its reciprocal = 1

To find the average, we add the two values and divide by 2:

(N + 1/N) / 2 = 1

Now we can simplify the equation:

Multiply both sides of the equation by 2:

N + 1/N = 2

Multiply through by N to eliminate the fraction:

N^2 + 1 = 2N

Next, move all terms to one side to set the equation to zero:

N^2 - 2N + 1 = 0

This is a quadratic equation. To solve it, we can either factor it, complete the square, or use the quadratic formula.

Factoring the equation, we have:

(N - 1)(N - 1) = 0

This yields a repeated solution, N = 1. Therefore, the number N is 1.

To summarize:

If the average of a number N and its reciprocal is 1, the number N is 1.