A three variables inequality

$\sqrt{(x + y)(x + z)} + \sqrt{(x + y)(y + z)} + \sqrt{(z + y)(x + z)} \geq x + y + z + \sqrt{3xy + 3yz + 3zx}$

Inequalities
Ailk Ailk
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  • Savionf Savionf
    +3

    This is a very challenging question. It should be offered a fair bounty.

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