If a - b = 3 and a3 - b3 = 999, then Find the value of a2 - b2.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 63.
a - b = 3 and a3 - b3 = 999
a3 - b3 = (a - b) {(a - b)2 + 3ab}
⇒ 999 = 3(9 + 3ab)
⇒ 324/3 = ab
ab = 108
(a + b)2 = (a - b)2 + 4ab
⇒ (a + b)2 = 9 + 4 × 108
⇒ (a + b)2 = 441
⇒ a + b = 21
a2 - b2 = (a + b)(a - b) = 3 × 21 = 63