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a,b,c≥0,
(1)${b^2} + {c^2} > 2\left( {{b^2}{c^2} + {c^2}{a^2} + {a^2}{b^2}} \right)$,求证：${\rm{b}} + {\rm{c}} - {\rm{a}} \ge - {1 \over {\sqrt 2 }}$
(2)a≥b,a≥c,${b^2} + {c^2} > 2\left( {{b^2}{c^2} + {c^2}{a^2} + {a^2}{b^2}} \right)$,求证：${\rm{b}} + {\rm{c}} - {\rm{a}} \le {1 \over {\sqrt 3 }}$
(3)a≥b,a≥c,b+c≥a,求证：${b^2} + {c^2} - 2\left( {{b^2}{c^2} + {c^2}{a^2} + {a^2}{b^2}} \right) \le {1 \over 6}$ |
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