The sum of a non zero real number and its reciprocal is 2. What is the value of that number?

Introduction / Context:
This problem checks understanding of simple algebraic equations involving a number and its reciprocal. Questions of the form x + 1 / x equal to some constant appear frequently in aptitude and competitive exams. Being comfortable with converting such verbal statements into equations and solving quadratic equations quickly is very important for speed and accuracy.

Given Data / Assumptions:
- Let the unknown non zero real number be x. - The sum of the number and its reciprocal is 2, so x + 1 / x = 2. - x is non zero, so division by x is valid.

Concept / Approach:
- Translate the statement into an equation: x + 1 / x = 2. - Clear the denominator by multiplying both sides by x, which is allowed because x is non zero. - This will give a quadratic equation in x. - Solve the quadratic and choose the solution that fits all conditions.

Step-by-Step Solution:
Step 1: Start from the equation x + 1 / x = 2. Step 2: Multiply both sides by x to remove the denominator: x * x + 1 = 2x. Step 3: This simplifies to x^2 + 1 = 2x. Step 4: Rearrange all terms to one side to get a standard quadratic equation: x^2 - 2x + 1 = 0. Step 5: Factor the quadratic: x^2 - 2x + 1 = (x - 1)^2 = 0. Step 6: Solve (x - 1)^2 = 0 to get the single solution x = 1.

Verification / Alternative check:
Substitute x = 1 back into the original relation. Then x + 1 / x becomes 1 + 1 / 1 which is 1 + 1 = 2. This matches the given condition exactly, so x = 1 is correct. There is no other solution because the quadratic has a repeated root, meaning there is only one distinct solution.

Why Other Options Are Wrong:
Option B: If x = 2, then x + 1 / x = 2 + 1 / 2 = 2.5, which is not equal to 2. Option C: If x = -1, then x + 1 / x = -1 + (-1) = -2, which does not satisfy the condition. Option D: If x = 4, then x + 1 / x = 4 + 1 / 4 = 4.25, which is incorrect. Option E: If x = 0.5, then x + 1 / x = 0.5 + 2 = 2.5, so this is also not valid.

Common Pitfalls:
- Forgetting that x must be non zero and multiplying by x without noting that condition. - Making sign errors when moving terms to one side of the equation. - Not recognizing that a perfect square quadratic like (x - 1)^2 = 0 has only one distinct solution.

Final Answer:
The required non zero number whose sum with its reciprocal equals 2 is 1.