Prove that $$\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c} \ge \dfrac{a}{b}+\dfrac{b}{c}+\dfrac{c}{a}+2(a+b+c)$$for the all $a,b,c$ positive real numbers satisfying $a^2+b^2+c^2+2abc \le 1$.
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Tags: Inequality
Prove that $$\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c} \ge \dfrac{a}{b}+\dfrac{b}{c}+\dfrac{c}{a}+2(a+b+c)$$for the all $a,b,c$ positive real numbers satisfying $a^2+b^2+c^2+2abc \le 1$.