If a + b + c = 0, then a2 + ab + b2 is equal to :(a) b2 – bc + c2 (

1.	If a + b + c = 0, then a2 + ab + b2 is equal to :(a) b2 – bc + c2 (b) c2 – ab (c) b2 + bc + c2 (d) 0
Answer» (c) c² – ab If a + b + c = 0, then a³ + b³ + c³ – 3abc = 0 ⇒ (a + b) (a² – ab + b²) + c³ = 3abc ⇒ (– c) (a² – ab + b²) + c³ = 3abc [∵ (a + b) = – c] ⇒ a² – ab + b² – c² = – 3ab ⇒ a² – ab + b² + 2ab – c² = – 3ab + 2ab = a² + ab + b² = c² – ab

If a + b + c = 0, then a2 + ab + b2 is equal to :(a) b2 – bc + c2 (b) c2 – ab (c) b2 + bc + c2 (d) 0

Answer»

(c) c² – ab

If a + b + c = 0, then a³ + b³ + c³ – 3abc = 0

⇒ (a + b) (a² – ab + b²) + c³ = 3abc

⇒ (– c) (a² – ab + b²) + c³ = 3abc [∵ (a + b) = – c]

⇒ a² – ab + b² – c² = – 3ab

⇒ a² – ab + b² + 2ab – c² = – 3ab + 2ab = a² + ab + b² = c² – ab