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Category: Algebra

e-x-gt-1-x-x-gt-0-set-x-pi-e-1-e-pi-e-1-gt-pi-e-e-pi-e-gt-pi-e-pi-e-e-gt-pi-e-e

Question Number 189886 by mnjuly1970 last updated on 23/Mar/23 $$ \\ $$$$\:\:{e}^{\:{x}} \:>\:\mathrm{1}+\:{x}\:\:\:\:\left(\forall\:{x}\:>\mathrm{0}\:\right) \\ $$$$\:\:\:{set}:\:{x}=\sqrt{\frac{\pi}{{e}}}\:−\mathrm{1} \\ $$$$\:\:\:\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:−\mathrm{1}} >\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:\Rightarrow\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \:>\:\sqrt{\pi}\: \\ $$$$\:\:\:\:\:\:\left(\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \right)^{\:\sqrt{{e}}} >\:\sqrt{\pi}\:^{\:\sqrt{{e}}} \:\Rightarrow\:{e}^{\:\sqrt{\pi}} \:>\:\sqrt{\pi\:}\:^{\:\sqrt{{e}}}…

Question-58816

Question Number 58816 by Tawa1 last updated on 30/Apr/19 Answered by Kunal12588 last updated on 30/Apr/19 $${from}\:{looking}\:{the}\:{graph}\:{we}\:{can}\:{say}\:{that} \\ $$$${maxima}\:{of}\:{function}\:{is}\:{at}\:\:{x}=\mathrm{2} \\ $$$$\left.{for}\:{A}\right) \\ $$$$\frac{{d}\left({f}\left({x}\right)\right)}{{dx}}=\mathrm{0}\:\:\:\:\:\left[{for}\:{minima}\:{or}\:{maxima}\right] \\ $$$$−\frac{\mathrm{1}}{\mathrm{3}}×\mathrm{2}\left({x}−\mathrm{2}\right)\left(\mathrm{1}\right)=\mathrm{0}…

Question-189858

Question Number 189858 by Shrinava last updated on 23/Mar/23 Answered by mr W last updated on 23/Mar/23 $${f}\left({x}\right)={x}^{\frac{\mathrm{1}}{{x}}} \:{is}\:{strictly}\:{increasing}\:{for}\:\mathrm{0}<{x}<{e} \\ $$$${since}\:\mathrm{1}<\sqrt{{e}}<\sqrt{\pi}<{e}, \\ $$$$\left(\sqrt{{e}}\right)^{\frac{\mathrm{1}}{\:\sqrt{{e}}}} <\left(\sqrt{\pi}\right)^{\frac{\mathrm{1}}{\:\sqrt{\pi}}} \\…

367-25-397-45-484-79-

Question Number 58780 by hhghg last updated on 29/Apr/19 $$\mathrm{367}×\mathrm{25} \\ $$$$\mathrm{397}×\mathrm{45} \\ $$$$\mathrm{484}×\mathrm{79} \\ $$ Answered by ajfour last updated on 30/Apr/19 $$\mathrm{3}×\mathrm{25}×\mathrm{100}+\mathrm{6}×\mathrm{25}×\mathrm{10}+\mathrm{7}×\mathrm{25} \\…

x-x-y-y-19-x-y-y-x-15-find-x-y-x-x-y-y-133-y-x-x-y-30-find-x-y-xy-x-y-53-x-y-23-find-x-y-

Question Number 124314 by liberty last updated on 02/Dec/20 $$\begin{cases}{{x}\sqrt{{x}}\:+{y}\sqrt{{y}}\:=\:\mathrm{19}}\\{{x}\sqrt{{y}}\:+{y}\sqrt{{x}}\:=\:\mathrm{15}}\end{cases}.\:{find}\:{x}+{y} \\ $$$$\:\begin{cases}{{x}\sqrt{{x}}\:+{y}\sqrt{{y}}\:=\:\mathrm{133}}\\{{y}\sqrt{{x}}\:−\:{x}\sqrt{{y}}\:=\:\mathrm{30}}\end{cases}.\:{find}\:{x}+{y}+{xy} \\ $$$$\:\begin{cases}{\sqrt{{x}}\:+{y}\:=\:\mathrm{53}}\\{{x}\:+\:\sqrt{{y}}\:=\:\mathrm{23}}\end{cases}.\:{find}\:{x}+{y} \\ $$ Commented by Dwaipayan Shikari last updated on 02/Dec/20 $$\sqrt{{x}}+{y}=\mathrm{53}…