câu lấy 10 điểm

C

conga222222

$\eqalign{
& 2\left( {{a^2}{b^2} + {b^2}{c^2} + {c^2}{a^2}} \right) = {\left( {{a^2} + {b^2} + {c^2}} \right)^2} - {a^4} - {b^4} - {c^4} = 9 - \left( {{a^4} + {b^4} + {c^4}} \right) \cr
& bdt:a + b + c \ge {a^2}{b^2} + {b^2}{c^2} + {c^2}{a^2} \cr
& \leftrightarrow 2\left( {a + b + c} \right) \ge 2\left( {{a^2}{b^2} + {b^2}{c^2} + {c^2}{a^2}} \right) = 9 - \left( {{a^4} + {b^4} + {c^4}} \right) \cr
& \leftrightarrow {a^4} + 2a + {b^4} + 2b + {c^4} + 2c \ge 9 \cr
& \cos i: \cr
& {a^4} + 2a = {a^4} + a + a \ge 3{a^2} \cr
& ...... \cr
& \to {a^4} + 2a + {b^4} + 2b + {c^4} + 2c \ge 3{a^2} + 3{b^2} + 3{c^2} = 9 \to dung\; \to dpcm \cr} $
 
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