Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?
Option 1: $a^2+b^2+c^2-3abc$
Option 2: $0$
Option 3: $3abc$
Option 4: $a^2+b^2+c^2-ab-bc-ca$
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Answer (1)
23rd Jan, 2024
Correct Answer: $3abc$
Solution :
Using the identity: $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$.
If $a + b + c = 0$,
$a^3 + b^3 + c^3 - 3abc = 0$
⇒ $a^3 + b^3 + c^3 = 3abc$
Hence, the correct answer is $3abc$.
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