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Question Number 116798 by mnjuly1970 last updated on 06/Oct/20

$$...calculus...$$$$$$$$a,b,c\in {\mathbb{R}}^{+}::$$$$$$$$find$$$$$$$$min(\sqrt{\frac{b+c}{a}}+\sqrt{\frac{a+c}{b}}+\sqrt{\frac{a+b}{c}})=???$$$$$$$$...m.n.1970...$$$$$$

Answered by mr W last updated on 06/Oct/20

$$⩾\sqrt{\frac{2\sqrt{bc}}{a}}+\sqrt{\frac{2\sqrt{ac}}{b}}+\sqrt{\frac{2\sqrt{ab}}{c}}$$$$⩾3\sqrt[3]{\sqrt{\frac{8abc}{abc}}}=3\sqrt{2}$$

Commented by mnjuly1970 last updated on 07/Oct/20

$$tayyeballahthankyou..$$

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