Q511
If a - b = 4 and a3 - b3 = 88, then find the value of a2 - b2.
A.
6√6
B.
9√6
C.
7√6
D.
8√6
AnswerAnswer: Option D
Solution
Answer: Option D
Solution:
a - b = 4, a3 - b3 = 88then a2 - b2 = ?
(a - b)3 = a3 - b3 - 3ab(a - b)
64 = 88 - 12(ab)
ab = 2
(a + b)2 - (a - b)2 = 4ab
(a + b)2 - 16 = 4 × 2
(a + b)2 = 24
(a + b) = 2√6
a2 - b2 = (a + b) × (a - b) = 2√6 × 4 = 8√6