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E

eye_smile

$(a-1)(b-1)(c-1) \ge 0$

\Leftrightarrow $abc-ab-bc-ca+5 \ge 0$

$(a-3)(b-3)(c-3) \le 0$

\Leftrightarrow $abc-3(ab+bc+ca)+27 \le 0$

\Rightarrow $2(ab+bc+ca) \ge 22$

\Rightarrow $a^2+b^2+c^2 \le 14$

 
H

huradeli

eye_smile said:
$(a-1)(b-1)(c-1) \ge 0$

\Leftrightarrow $abc-ab-bc-ca+5 \ge 0$

$(a-3)(b-3)(c-3) \le 0$

\Leftrightarrow $abc-3(ab+bc+ca)+27 \le 0$

\Rightarrow $2(ab+bc+ca) \ge 22$

\Rightarrow $a^2+b^2+c^2 \le 14$
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