Question : If a + b + c = 0, the value of (a3 + b3 + c3) is:
Option 1: abc
Option 2: 2abc
Option 3: 3abc
Option 4: 0
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Correct Answer: 3abc
Solution : Given: a + b + c = 0 a 3 + b 3 + c 3 – 3abc = (a + b + c)(a 2 + b 2 + c 2 – ab – bc – ca) ⇒ a 3 + b 3 + c 3 – 3abc = (0)(a 2 + b 2 + c 2 – ab – bc – ca) ⇒ 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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Question : a3 + b3 + c3 = 3abc if _________.
Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?
Question : If (a + b + c) = 12 and (ab + bc + ca) = 47, find the value of (a3 + b3 + c3 – 3abc).
Question : If a( a + b + c) = 45, b( a + b + c) = 75, and c( a + b + c) =105, then what is the value of a2 + b2 + c2?
Question : What is the possible value of (a + b + c) – 3, if a2 + b2 + c2 = 9 and ab + bc + ca = 8?
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