Question

Sum of a number and its reciprocal is 2. Then what is the number ?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer:

A. 1

The number is 1.

1. Set up the equation
Let the unknown number be $x$. Its reciprocal is $\frac{1}{x}$.
$x + \frac{1}{x} = 2$

2. Eliminate the fraction
Multiply the entire equation by $x$ to remove the denominator:
$x(x) + x\left(\frac{1}{x}\right) = 2(x)$
$$x^2 + 1 = 2x$

3. Form a quadratic equation
Move $2x$ to the left side to set the equation to zero:
$x^2 - 2x + 1 = 0$

4. Factor the equation
The expression $x^2 - 2x + 1$ is a perfect square trinomial, which factors into:
$(x - 1)^2 = 0$

5. Solve for $x$
Take the square root of both sides:
$x - 1 = 0$
$x = 1$