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Category: Algebra

x-1-x-x-2-1-x-x-1-

Question Number 135108 by bramlexs22 last updated on 10/Mar/21 $$\left(\sqrt{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}}\:\right)^{\mathrm{x}^{\mathrm{2}} } \:=\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} \\ $$ Answered by MJS_new last updated on 10/Mar/21 $${x}^{\mathrm{2}} ={x}+\mathrm{1}\:\Leftrightarrow\:\frac{{x}−\mathrm{1}}{{x}}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\…

Twin-of-Q-3943-Three-circles-are-drawn-in-a-plane-in-such-a-way-that-a-closed-region-is-produced-which-is-not-included-in-any-of-the-circles-Determine-the-area-of-this-region-Circles-Radii-Cente

Question Number 4036 by Rasheed Soomro last updated on 27/Dec/15 $$\mathrm{Twin}\:\mathrm{of}\:\mathrm{Q}#\mathrm{3943} \\ $$$$\mathrm{Three}\:\mathrm{circles}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{in}\:\mathrm{a}\:\mathrm{plane} \\ $$$$\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{region} \\ $$$$\mathrm{is}\:\mathrm{produced}\:\mathrm{which}\:\mathrm{is}\:\mathrm{not}\:\mathrm{included} \\ $$$$\mathrm{in}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circles}.\:\mathrm{Determine}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{this}\:\mathrm{region}. \\ $$$$\underset{−} {\mathrm{Circles}\:\mid\:\mathrm{Radii}\:\mid\:\mathrm{Centers}\:} \\…

Find-x-such-that-x-2-5x-5-x-2-21x-10-1-

Question Number 4013 by Yozzii last updated on 26/Dec/15 $${Find}\:{x}\:{such}\:{that}\:\left({x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{5}\right)^{{x}^{\mathrm{2}} −\mathrm{21}{x}+\mathrm{10}} =\mathrm{1}. \\ $$ Commented by 123456 last updated on 26/Dec/15 $${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{5}=\mathrm{1}\Leftrightarrow{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{4}=\mathrm{0}…