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Question
If 3x – 4y = 5 and xy = 3, find : 27x3 – 64y3.
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Solution
27x3 – 64y3 = (3x)3 – (4y)3
= (3x − 4y)3 (3x − 4y)3 + 3 (3x) (4y) (3x − 4y) ......[ ∵ a3 − b3 = (a − b)3 + 3ab(a − b)]
= (5)3 + 36(xy) (3x − 4y)
= 125 + 36 (3) (5)
= 125 + 540
= 665
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