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Question
Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
Solution
(28)3 + (–15)3 + (–13)3
Let x = 28, y = −15 and z = −13
It can be observed that,
x + y + z = 28 + (−15) + (−13)
= 28 − 28
= 0
It is known that if x + y + z = 0, then
x3 + y3 + z3 = 3xyz
∴ (28)3 + (–15)3 + (–13)3
= 3(28)(–15)(–13)
= 16380
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