Question
If (a + b + c) = 9, find (a – 4)3 + (b
– 2)3 + ( c – 3)3 - 3(a – 4 ) (b – 2 ) (c – 3)?Solution
a + b + c = 9 a + b + c = 4 + 2 + 3 (a – 4 ) + (b – 2) + (c – 3) = 0 If x + y + z = 0 x2 + y2 + z2 = 3xyz (a – 4)3 + (b – 2)3 + ( c – 3)3 = 3(a – 4 ) (b – 2 ) (c – 3) (a – 4)3 + (b – 2)3 + ( c – 3)3 - 3(a – 4 ) (b – 2 ) (c – 3) = 0
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