Question

without actually calculating the cubes, deduse the value of (-12^3) +5^3+7^3​

Answer 1

We know the corollary: if a+b+c=0 then a

3

+b

3

+c

3

=3abc

Using the above corollary taking a=−12, b=7 and c=5, we have a+b+c=−12+7+5=0 then the value of (−12)

3

+7

3

+5

3

is:

(−12)

3

+7

3

+5

3

=3(−12×7×5)=−1260

Hence, (−12)

3

+7

3

+5

3

=−1260

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