If a3 - b3 = 2349 and (a - b) = 9, then (a+b)2 - ab is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 261.
We knows that, (a - b)3 = a3 - b3 - 3ab(a - b)
⇒ (a - b)3 = a3 - b3 - 3ab(a - b) = (9)3 = 2349 - 3ab(9)
⇒ 729 = 2349 - 27ab
⇒ ab = 60
We knows that,
⇒ (a - b)2 = (a + b)2 - 4ab
⇒ (9)2 = (a + b)2 - ab - 3ab
⇒ 81 + 180 = (a + b)2 - ab
⇒ (a + b)2 - ab = 261.