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Multiple Choice Questions

If a b c 0 then the value of a b ndash c 2 b c ndash a 2 c a ndash b 2 is ........

Mathematics (NDA) Algebra

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If a + b + c = 0, then the value of (a + b – c)² + (b + c – a)² + (c + a – b)² is

8 abc

4(a² + b² + c²)

4(ab + bc + ca)

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Explanation:

Given, a + b + c = 0
∴ a + b = – c, b + c = – a, c + a = – b
∴ (a + b – c)² + (b + c – a)² + (c + a – b)²
⇒ (– c – c)² + (– a – a)² + (– b – b)²
⇒ (– 2c)² + (– 2a)² + (–2b)²
⇒ 4c² + 4a² + 4b² = 4(a² + b² + c ²)