# My Problems #15

Algebra Level 4

$$\sqrt{\dfrac{a^2+b^2}{a+b}}+\sqrt{\dfrac{b^2+c^2}{c+b}}+\sqrt{\dfrac{a^2+c^2}{a+c}} +3 \leq k \left(\sqrt{a+b} + \sqrt{c+b} +\sqrt{a+c} \right)$$

Consider all sets of positive real numbers $$a,b,c$$ such that $$ab + bc + ca ≤ 3abc$$. What is the smallest value of $$k$$ such that the inequality above is fulfilled?

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