Two numbers have a sum of 10 and a product of 20. What is the value of the sum of their reciprocals, that is, (1 / a) + (1 / b)?

Introduction / Context:The task is to compute the sum of reciprocals of two numbers when their sum and product are known. This is a standard identity application in algebra and aptitude tests, allowing a quick computation without explicitly finding the two numbers themselves.

Given Data / Assumptions:

• a + b = 10.
• ab = 20.
• We need (1 / a) + (1 / b).

Concept / Approach:Use the identity (1 / a) + (1 / b) = (a + b) / (ab). This follows from putting the two fractions over a common denominator ab. Then, insert the given sum and product directly into the identity to compute a concise result.

Step-by-Step Solution:

Verification / Alternative check:If desired, solve t^2 − 10t + 20 = 0 for actual numbers; they will yield a + b = 10 and ab = 20, and their reciprocals will still sum to 1/2 by the same identity.

Why Other Options Are Wrong:1, 3/5, 11/6, and 3/2 do not equal (a + b) / (ab) with the given values. They arise from arithmetic slips or incorrect identities.

Common Pitfalls:Attempting to find each number individually is unnecessary and can introduce errors. Forgetting the identity or inverting the ratio (ab)/(a + b) is another common mistake.

Final Answer:1/2