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Question

Without actually calculating the cubes, find the value of (12)3+(7)3+(5)3


A

0

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B

-36

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C

-1620

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D

-1260

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Solution

The correct option is D

-1260


x3+y3+z33xyz=(x+y+z)(x2+y2+z2xyyzzx)

When (x+y+z)=0

x3+y3+z3=3xyz

12+7+5=0

(12)3+(7)3+(5)3=3(12)(7)(5)=1260


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