Question : If $a=331, b=336$ and $c=–667$, then the value of $a^3+b^3+c^3–3abc$ is:
Option 1: 1
Option 2: 63
Option 3: 3
Option 4: 0
Answer (1)
23rd Jan, 2024
Correct Answer: 0
Solution :
$a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$
If $a+b+c=0$, then $a^3+b^3+c^3-3abc=0$
Here $a+b+c= 331+336-667=0$
So,
$a^3+b^3+c^3-3abc=0$
Hence, the correct answer is 0.
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