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Question
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
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Solution
(–12)3 + (7)3 + (5)3
Let x = −12, y = 7 and z = 5
It can be observed that,
x + y + z = − 12 + 7 + 5 = 0
It is known that if x + y + z = 0, then
x3 + y3 + z3 = 3xyz
∴ (–12)3 + (7)3 + (5)3
= 3[(–12)(7)(5)]
= 3[–420]
= –1260
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