Mathematics
Without actually calculating the cubes, find the values of:
(i) (27)3 + (-17)3 + (-10)3
(ii) (-28)3 + (15)3 + (13)3
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Answer
(i) Let a = 27, b = -17, c = -10
Then,
a + b + c = 27 - 17 - 10 = 0
Thus, a3 + b3 + c3 = 3abc
∴ (27)3 + (-17)3 + (-10)3 = 3(27)(-17)(-10) = 13770
(ii) Let a = -28, b = 15, c = 13
Then,
a + b + c = -28 + 15 + 13 = 0
Thus, a3 + b3 + c3 = 3abc
∴ (-28)3 + (15)3 + (13)3 = 3(-28)(15)(13) = -16380
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