Question Number 60946 by Tawa1 last updated on 27/May/19 $$\mathrm{Find}\:\mathrm{x}:\:\:\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:=\:\:\mathrm{2x} \\ $$ Commented by Prithwish sen last updated on 27/May/19 $$\mathrm{x}=\mathrm{2} \\ $$ Commented…
Question Number 126482 by ayyoubmaths last updated on 20/Dec/20 Answered by Dwaipayan Shikari last updated on 20/Dec/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{cosx}−\mathrm{1}}{{x}}\right)=−\frac{\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{{x}}=−\frac{{x}^{\mathrm{2}} }{\mathrm{2}{x}}=\mathrm{0} \\ $$ Terms of…
Question Number 192009 by universe last updated on 05/May/23 $$\:\:\:\:\:{if}\:\:{a}>\mathrm{1}\:,\:{show} \\ $$$$\:\:\:\:\:\frac{\underset{{k}=\mathrm{1}} {\overset{{a}^{\mathrm{2}} −\mathrm{1}} {\sum}}\:\:\sqrt{{a}+\sqrt{{k}}}}{\underset{{k}=\mathrm{1}} {\overset{{a}^{\mathrm{2}} −\mathrm{1}} {\sum}}\:\:\sqrt{{a}−\sqrt{{k}}}}\:\:\:=\:\:\:\sqrt{\mathrm{2}}\:\:+\:\:\mathrm{1} \\ $$ Answered by Skabetix last updated…
Question Number 60910 by Tawa1 last updated on 27/May/19 Commented by Rasheed.Sindhi last updated on 27/May/19 $${S}\mathrm{olve}\:\mathrm{the}\:\mathrm{equation}\:\:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} \:−\:\mathrm{4x}\left(\mathrm{x}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:\:=\:\:\:\mathrm{0} \\ $$$$ \\ $$$${x}^{\mathrm{4}} +{x}^{\mathrm{2}}…
Question Number 60905 by necx1 last updated on 27/May/19 $${if}\:{x}+\frac{\mathrm{1}}{{x}}=\sqrt{\mathrm{3}}.{find} \\ $$$${x}^{\mathrm{24}} +{x}^{\mathrm{18}} +{x}^{\mathrm{6}} +\mathrm{1} \\ $$ Answered by ajfour last updated on 27/May/19 $${E}={x}^{\mathrm{24}}…
Question Number 126430 by TITA last updated on 20/Dec/20 $$\mathrm{log}\:_{\mathrm{6}} ^{\mathrm{15}} =\mathrm{a}\:\:\:\mathrm{log}\:_{\mathrm{12}} ^{\mathrm{18}} =\mathrm{b}\:\:\mathrm{find}\:\mathrm{log}\:_{\mathrm{25}} ^{\mathrm{24}} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b} \\ $$ Commented by TITA last updated on…
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Question Number 191950 by Shrinava last updated on 04/May/23 $$\sqrt{\mathrm{a}}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:\:\:\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{2}} −\mathrm{a}−\sqrt{\mathrm{a}}\:=\:? \\ $$ Answered by AST last updated on 04/May/23 $$\frac{\mathrm{1}}{\:\sqrt{{a}}−\mathrm{1}}=\frac{\sqrt{{a}}+\mathrm{1}}{{a}−\mathrm{1}}={a}\Rightarrow{a}^{\mathrm{2}} −{a}−\sqrt{{a}}=\mathrm{1} \\ $$ Terms…
Question Number 191947 by universe last updated on 04/May/23 $${prove}\:{that} \\ $$$$\sqrt{{a}+{b}\sqrt{{a}−{b}\sqrt{{a}+{b}\sqrt{{a}−{b}\sqrt{…}}}}}\:\:=\:\:\frac{\sqrt{\mathrm{4}{a}−\mathrm{3}{b}^{\mathrm{2}} }+{b}}{\mathrm{2}} \\ $$ Answered by ajfour last updated on 05/May/23 $${Let}\:{s}=\sqrt{{a}+{b}\sqrt{{a}−{bs}}}=\frac{{b}+\sqrt{\mathrm{4}{a}−\mathrm{3}{b}^{\mathrm{2}} }}{\mathrm{2}} \\…
Question Number 191946 by mustafazaheen last updated on 04/May/23 $$\frac{\mathrm{fof}^{−\mathrm{1}} \left(\mathrm{5}\right)+\mathrm{fof}^{−\mathrm{1}} \left(\mathrm{15}\right)}{\mathrm{fof}^{−\mathrm{1}} \left(\mathrm{5}\right)}=? \\ $$ Answered by horsebrand11 last updated on 04/May/23 $$=\:\mathrm{4} \\ $$…