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If a - b = 18 and a3 - b3 =...

This question belongs to Arithmetic Ability Algebra
Algebra
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If a - b = 18 and a3 - b3 = 324, then find the value of ab.

Answer & Solution
Correct Answer: Option A
a - b = 18, a3 - b3 = 324
(a - b)(a2 + b2 + ab) = 324
⇒ 18[(a - b)2 + 3ab] = 324
⇒ 324 + 3ab = 18
⇒ 3ab = 18 - 324
⇒ 3ab = -306
⇒ ab = -102
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