JEE Main Maths: Basic Algebra questions with solutions

Q1. Given x - y = 2 and x*y = 24, find the value of 1/x + 1/y.

1. 1/12
2. -1/12
3. 1/6
4. 2/24

Answer: 1/12

We need (x + y)/(x*y). From x - y = 2 and xy = 24: (x + y)² = (x - y)² + 4xy = 4 + 96 = 100, so x + y = 10 (taking the positive value; e.g. x = 6, y = 4). Then 1/x + 1/y = (x + y)/(xy) = 10/24 = 5/12. Hmm 10/24 = 5/12, not 1/12. Recheck: with x=6,y=4: 1/6+1/4 = 2/12+3/12 = 5/12. So correct value is 5/12.