Question

When a number is subtracted from 2, the result is equal to the reciprocal of the original number. Find the number.​

Answer 1

To find the number, set up an equation and solve it using algebraic steps.

Step-by-step explanation:

To find the number, let's call it 'x', we can set up an equation based on the given information. The equation is: 2 - x = 1/x. Now, let's solve this equation:

1. First, let's get rid of the fraction by multiplying both sides of the equation by 'x'. This gives us: 2x - x^2 = 1.
2. Next, let's rearrange the equation and make it a quadratic equation by moving all terms to one side: x^2 - 2x + 1 = 0.
3. Finally, let's solve this quadratic equation by factoring or using the quadratic formula. In this case, the equation factors to (x - 1)^2 = 0. Therefore, the only solution is x = 1.

So, the number is 1.