Prove that b2c2+c2a2+a2+b2>abc×(a+b+c)(a,b,c>0) .

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Prove that {b}^{{2}}{c}^{{2}}+{c}^{{2}}{a}^{{2}}+{a}^{{2}}+{b}

Question

Prove that $b^{2} c^{2} + c^{2} a^{2} + a^{2} + b^{2} > a b c \times (a + b + c) (a, b, c > 0)$ .

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Prove that

b^{2} c^{2} + c^{2} a^{2} + a^{2} + b^{2} > a b c \times (a + b + c) (a, b, c > 0)

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Question Text

Prove that

b^{2} c^{2} + c^{2} a^{2} + a^{2} + b^{2} > a b c \times (a + b + c) (a, b, c > 0)