If a - b = 3 and a2 + b2 = 29, find the value of ab.
2025
If a - b = 3 and a2 + b2 = 29, find the value of ab.
- A.
10
- B.
12
- C.
14
- D.
16
Attempted by 33 students.
Show answer & explanation
Correct answer: A
Solution:
Use the identity (a - b)^2 = a^2 + b^2 - 2ab. Rearranging gives 2ab = a^2 + b^2 - (a - b)^2.
Substitute the given values: a^2 + b^2 = 29 and (a - b)^2 = 3^2 = 9, so 2ab = 29 - 9 = 20.
Therefore ab = 20 / 2 = 10.