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Category: Algebra

Q-179570-Posted-by-Infinityaction-30-10-2022-find-the-minimum-of-f-x-f-x-x-2-4-x-2-8x-12-x-25-x-2-4-x-2-16x-16-x-80-f-x-x-4-2-2-x-3-2-

Question Number 179717 by a.lgnaoui last updated on 01/Nov/22 $$\mathrm{Q}\:\mathrm{179570}\:\left({Posted}\:{by}\:\mathrm{Infinityaction}\:\mathrm{30}.\mathrm{10}.\mathrm{2022}\right) \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{4}}{\mathrm{x}^{\mathrm{2}} }−\mathrm{8x}−\frac{\mathrm{12}}{\mathrm{x}}+\mathrm{25}}\:+\sqrt{\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{4}}{\mathrm{x}^{\mathrm{2}} }−\mathrm{16x}−\frac{\mathrm{16}}{{x}}+\mathrm{80}}\: \\ $$$$−−−−−−−−−−−−−−−−−− \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{2}} +\left(\frac{\mathrm{2}}{\mathrm{x}}−\mathrm{3}\right)^{\mathrm{2}} }\:\:+\sqrt{\left(\mathrm{x}−\mathrm{8}\right)^{\mathrm{2}} +\left(\frac{\mathrm{2}}{\mathrm{x}}−\mathrm{4}\right)^{\mathrm{2}}…