If a2 + b2 = 82 and ab = 9, then a possible value of a3 + b3 is :
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 730.
We know that,
(a + b)2 = a2 + b2 + 2ab
(a + b)3 = a3 + b3 + 3b(a + b)
According to the question
⇒ (a + b)2 = a2 + b2 + 2ab
⇒ (a + b)2 = 82 + 2 × 9
⇒ (a + b)2 = 100
⇒ (a + b) = 10
Now,
⇒ (a + b)3 = a3 + b3 + 3ab(a + b)
⇒ (10)3 = a3 + b3 + 3 × 9 × 10
⇒ 1000 = a3 + b3 + 270
⇒ a3 + b3 = 1000 - 270 = 730
So,
⇒ a3 + b3 = 730