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प्रश्न
If a + b = 6 and ab = 8, find: a3 + b3.
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उत्तर
a + b = 6, ab = 8,
⇒ (a + b)3 = (6)3
Using the identity,
⇒ 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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