Category: Algebra

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}}} \\…

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}…

Question Number 124312 by liberty last updated on 02/Dec/20 $$\:\:\:\:\mathrm{3}^{{x}} \:+\:\mathrm{3}^{−{x}} \:=\:\mathrm{3}\:−\left({x}−\mathrm{3}\right)^{\mathrm{2}} \\ $$$$\:{x}\:=?\: \\ $$ Answered by MJS_new last updated on 02/Dec/20 $$\mathrm{3}^{{x}} +\mathrm{3}^{−{x}}…

Question Number 58775 by MJS last updated on 29/Apr/19 $$\mathrm{solve}\:\mathrm{exactly}: \\ $$$${x}^{\mathrm{8}} −\mathrm{8}{x}^{\mathrm{7}} −\mathrm{16}{x}^{\mathrm{6}} +\mathrm{208}{x}^{\mathrm{5}} −\mathrm{152}{x}^{\mathrm{4}} −\mathrm{928}{x}^{\mathrm{3}} +\mathrm{704}{x}^{\mathrm{2}} +\mathrm{1088}{x}−\mathrm{368}=\mathrm{0} \\ $$ Terms of Service Privacy…

Question Number 58772 by hhghg last updated on 29/Apr/19 $$\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$ \\ $$ Answered by George Mark Samuel last updated on 29/Apr/19 $$\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{2}}{\mathrm{5}}=\frac{\mathrm{1}}{\mathrm{15}} \\…