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Question
If 2x - 3y = 10 and xy = 16; find the value of 8x3 - 27y3.
Sum
Solution
Given that 2x - 3y = 10, xy = 16
∴ (2x - 3y)3 = (10)3
⇒ 8x3 - 27y3 - 3 (2x) (3y) (2x - 3y) = 1000
⇒ 8x3 - 27 y3 -18xy (2x - 3y) = 1000
⇒ 8x3 - 27 y3 - 18 (16) (10) = 1000
⇒ 8x3 - 27 y3 - 2880 = 1000
⇒8x3 - 27 y3 = 1000 + 2880
⇒ 8x3 - 27 y3 =3880
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