Mathematics
Without actually calculating the cubes, find the value of each of the following:
(i) (-12)3 + (7)3 + (5)3
(ii) (28)3 + (-15)3 + (-13)3
Polynomials
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Answer
(i) (-12)3 + (7)3 + (5)3
Here,
-12 + 7 + 5 = 0
As, x + y + z = 0
So, x3 + y3 + z3 = 3xyz
= 3 x (-12) x 7 x 5
= -1260
Hence, (-12)3 + (7)3 + (5)3 = -1260
(ii) (28)3 + (-15)3 + (-13)3
Here,
= 28 + (-15) + (-13)
= 28 - 15 - 13
= 0
As, x + y + z = 0
So, x3 + y3 + z3 = 3xyz
= 3 x 28 x (-15) x (-13)
= 16380
Hence, (28)3 + (-15)3 + (-13)3 = 16380
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