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if-f-0-and-d-dx-f-x-2-f-x-2-and-f-0-1-find-f-x-if-f-x-4x-3-x-2-1-find-f-1-x-and-f-1-2-

Question Number 85653 by M±th+et£s last updated on 23/Mar/20 $${if}\:\:{f}\geqslant\mathrm{0}\:\:{and}\:\:\:\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)^{\mathrm{2}} =\left({f}'\left({x}\right)\right)^{\mathrm{2}} \:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${find}\:{f}\left({x}\right)\:\:\: \\ $$$$ \\ $$$${if}\:{f}\left({x}\right)=\frac{\mathrm{4}{x}^{\mathrm{3}} }{{x}^{\mathrm{2}} +\mathrm{1}}\:\:{find}\:{f}^{\:−\mathrm{1}} \left({x}\right)\:\:\:{and}\:\left({f}^{\:−\mathrm{1}} \right)^{'} \left(\mathrm{2}\right) \\ $$…

Proove-that-2-3-2-6-2-4-

Question Number 85649 by Hassen_Timol last updated on 23/Mar/20 $$\mathrm{Proove}\:\mathrm{that}\:: \\ $$$$ \\ $$$$\frac{\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}}{\mathrm{2}}\:=\:\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{2}}}{\mathrm{4}} \\ $$ Commented by mr W last updated on 23/Mar/20 $$\frac{\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}}{\mathrm{2}}=\frac{\sqrt{\mathrm{8}−\mathrm{4}\sqrt{\mathrm{3}}}}{\mathrm{4}}=\frac{\sqrt{\left(\sqrt{\mathrm{6}}\right)^{\mathrm{2}}…