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Question Number 151791 by mathdanisur last updated on 23/Aug/21

Answered by ghimisi last updated on 23/Aug/21

$$x_i^4+1⩾2x_i^2\Rightarrow x_i^4-x_i^2+1⩾x_i^2\Rightarrow \sqrt{x_i^4-x_i^2+1}+2x_i⩾3x_i$$$$\underset{i=1}{\sum ^n}(\sqrt{x_i^4-x_i^2+1}+2x_i)⩾\underset{i=1}{\sum ^n}3x_i=3\mathrm{\Sigma }{x}_i⩾3\cdot n\sqrt[n]{x_1{x}_2...x_n}=3n$$

Commented by mathdanisur last updated on 23/Aug/21

$$\mathrm{Thank}\mathrm{you}\mathbf{S}\mathrm{er}\mathrm{nice}$$

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