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Question
If a + b = 6 and ab=8, find : a3 + b3.
Solution
a + b = 6
⇒ (a + b)3 = (6)3
⇒ a3 + b3 + 3ab (a + b) = 216
⇒ a3 + b3 + 3×8 (6) = 216
⇒ a3 + b3 + 144 = 216
⇒ a3 + b3 = 216 − 144
⇒ a3 + b3 = 72
Alternative method :
(a + b)3 = a3 + b3 + 3ab (a + b)
⇒ (6)3 = a3 + b3 + 3×8 (6)
⇒ 216 = a3 + b3 + 144
⇒ 216 − 144 = a3 + b3
⇒ 72 = a3 + b3
⇒ a3 + b3 = 72
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