1.

If a + b + c = 3x, then find the value of (x – a)3 + (x – b)3 + (x – c)3 – 3(x – a)(x – b) (x – c).

Answer»

∵ (x – a) + (x – b) + (x – c) 

= 3x – (a + b + c) = 0 [ ∴ a + b + c = 3x] 

∴ (x – a)3 + (x – b)3 + (x – c)3 – 3(x – a) (x – b) (x – c) 

= 0 [ ∴ a + b + c = 0 => a3 + b3 + c3 – 3abc = 0]



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