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Question
Find 27a3 + 64b3, if 3a + 4b = 10 and ab = 2
Sum
Solution
3a + 4b = 10, ab = 2
(3a + 4b)3 = (3a)3 + 3(3a)2(4b) + 3(3a)(4b)2 + (4b)3
(27a3 + 64b3) = (3a + 4b)3 – 3 (3a)(4b)(3a + 4b)
∵ x3 + y3 = (x + y)3 – 3xy – (x + y)
= 103 – 36ab(10)
= 1000 – 36 × 2 × 10
= 1000 – 720
= 280
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