Show that
$a^{2} (1 + b^{2}) + b^{2} (1 + c^{2}) + c^{2} (1 + a^{2}) > 6 ab c$

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a^{2} (1 + b^{2}) + b^{2} (1 + c^{2}) + c^{2} (1 + a^{2}) > 6 ab c

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Question Text

Show that

a^{2} (1 + b^{2}) + b^{2} (1 + c^{2}) + c^{2} (1 + a^{2}) > 6 ab c

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