If a3 – b3 = 899 and a – b = 31, then (a – b)2 + 3ab is equal to:
Show answer & explanation
Correct answer: A
Explanation
Correct Answer is option 1 i.e. 29
|
Concept |
Understanding |
Application |
|
Formula: a3 – b3 = (a – b) × (a2 + b2 + ab) |
Given a3 – b3 = 899 and a – b = 31 |
a3 – b3 = (a – b) × (a2 + b2 + ab) ⇒ a3 – b3 = (a – b) × (a2 + b2 + ab + 2ab – 2ab) ⇒ a3 – b3 = (a – b) × ((a2 + b2 – 2ab) + 3ab) ⇒ a3 – b3 = (a – b) × ((a – b)2 + 3ab) Putting the values, (a3 – b3)/(a – b) = (a – b)2 + 3ab ⇒ 899/31 = (a – b)2 + 3ab ⇒ (a – b)2 + 3ab = 29 |