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Multiple Choice Questions

If a 2 234 b 3 121 and c ndash 5 355 then the value of a3 b3 c3 ndash 3abc is ........

Quantitative Aptitude (CCS) Algebra

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If a = 2.234, b = 3.121 and c = –5.355, then the value of a³ + b³ + c³ – 3abc is

-1

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Explanation:

a + b + c = 2.234 + 3.121 – 5.355 = 0
If a + b + c = 0, then a³ + b³ + c³ – 3abc = 0,
which can be proved as under
a + b = – c
Cubing both sides, we get
⇒ (a + b)³ = (– c)³
⇒ a³ + b³ + 3ab(a + b) = – c³
⇒ a³ + b³ + 3ab(– c) = – c³
⇒ a³ + b³ – 3abc = – c³
⇒ a³ + b³ + c³ – 3abc = 0