Tìm hàm số bậc hai y=f(x) thỏa mãn điều kiện

C

conga222222

$\eqalign{
& y = f\left( x \right) = a{x^2} + bx + c\;\left( {a \ne 0} \right) \cr
& f\left( {x - 1} \right) = a{\left( {x - 1} \right)^2} + b\left( {x - 1} \right) + c \cr
& f\left( {x + 1} \right) = a{\left( {x + 1} \right)^2} + b\left( {x + 1} \right) + c \cr
& \to f\left( {x - 1} \right) + f\left( x \right) + f\left( {x + 1} \right) = 3a{x^2} + 3bx + 3c + 2a = {x^2} \cr
& \to a = {1 \over 3};\;b = 0;\;c = - {2 \over 9} \cr} $
 
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