Question
If a − b = 4 and ab = 21, find the value of a3 − b3.
A. 312
B. 306
C. 316
D. 324
Answer: C. 316
Solution:
Given,
a − b = 4, ab = 21
Then,
⇒ (a − b)3 = a3 − 3a2b + 3ab2 − b3 = a3 − 3ab(a − b) − b3
⇒ 43 = a3 − b3 − 3(21)(4)
⇒ 64 + 252 = a3 − b3
∴ a3 − b3 = 316
Hence, the answer a3 − b3 = 316.