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Question
If a – b = 3 and ab = 10, find : a3 – b3.
Solution
a − b = 3
⇒ (a − b)3 = (3)3
⇒ a3 − b3 − 3ab (a − b) = 27
⇒ a3 − b3 − 3×10 (3) = 27
⇒ a3 − b3 − 90 = 27
⇒ a3 − b3 = 27 + 90
⇒ a3 − b3 = 117
Alternative Method :
(a − b)3 = a3 − b3 − 3ab (a − b)
⇒ (3)3 = a3 − b3 − 3×10 (3)
⇒ 27 = a3 − b3 − 90
⇒ 27 + 90 = a3 − b3
⇒ 117 = a3 − b3
⇒ a3 − b3 = 117
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