The sum of two numbers is 12 and their product is 35. Find the sum of their reciprocals.

Given data

• a + b = 12
• ab = 35

Concept / Approach

• Use the identity: 1/a + 1/b = (a + b)/ab.

Step-by-step calculation

1/a + 1/b = (a + b) / (ab) = 12 / 35Therefore, the required sum is 12/35.

Verification

Numbers satisfying a + b = 12 and ab = 35 are 5 and 7. Then 1/5 + 1/7 = (7 + 5)/35 = 12/35 ✔

Common pitfalls

• Adding reciprocals as 1/(a + b); that is incorrect.

Final Answer

12/35