Menu Close

Category: Algebra

Question-126482

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…

if-a-gt-1-show-k-1-a-2-1-a-k-k-1-a-2-1-a-k-2-1-

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-60910

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}}…

a-1-1-a-find-a-2-a-a-

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…

prove-that-a-b-a-b-a-b-a-b-4a-3b-2-b-2-

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}} \\…