Question Number 114676 by ZiYangLee last updated on 20/Sep/20 $$\mathrm{If}\:{a}^{\frac{\mathrm{1}}{\mathrm{2}}} −{a}^{−\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{1},\:\mathrm{prove}\:\mathrm{that}\:{a}+{a}^{−\mathrm{1}} =\mathrm{3} \\ $$ Answered by Olaf last updated on 20/Sep/20 $$\sqrt{{a}}+\frac{\mathrm{1}}{\:\sqrt{{a}}}\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\left(\sqrt{{a}}+\frac{\mathrm{1}}{\:\sqrt{{a}}}\right)^{\mathrm{2}}…
Question Number 49142 by AdqhK ÐQeQqQ last updated on 03/Dec/18 $${ln}\left(\infty\right)=?? \\ $$$${ln}\left(\mathrm{0}\right)=?? \\ $$$${ln}\left(−\mathrm{1}\right)=?? \\ $$ Answered by andyistic last updated on 03/Dec/18 $$\mathrm{ln}\:\infty\rightarrow\infty…
Question Number 114673 by Rasikh last updated on 20/Sep/20 $$\:\:\:\:\bigstar\:\:\:\mathrm{x}^{\mathrm{3}} −\mathrm{x}−\frac{\mathrm{1}}{\mathrm{6}}=\mathrm{0}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\mathrm{x}=? \\ $$ Commented by Dwaipayan Shikari last updated on 20/Sep/20 $${Q}\:\mathrm{114263} \\…
Question Number 114668 by bemath last updated on 20/Sep/20 $$\frac{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:+\:\frac{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\:\mathrm{98}\: \\ $$ Answered by som(math1967) last updated on 20/Sep/20 $$\frac{\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)^{\mathrm{2}}…
Question Number 114665 by mohammad17 last updated on 20/Sep/20 Answered by Olaf last updated on 20/Sep/20 $$−\mathrm{For}\:\mathrm{the}\:\mathrm{first}\:\mathrm{digit}\:\mathrm{we}\:\mathrm{have}\:\mathrm{5}\:\mathrm{solutions} \\ $$$$\left(\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\mathrm{or}\:\mathrm{5}\right). \\ $$$$−\mathrm{For}\:\mathrm{the}\:\mathrm{second}\:\mathrm{digit}\:\mathrm{we}\:\mathrm{have}\:\mathrm{4}\:\mathrm{solutions} \\ $$$$\left(\mathrm{no}\:\mathrm{repetition}\right) \\ $$$$−\mathrm{For}\:\mathrm{the}\:\mathrm{third}\:\mathrm{digit}\:\mathrm{we}\:\mathrm{have}\:\mathrm{3}\:\mathrm{solutions}…
Question Number 114660 by mohammad17 last updated on 20/Sep/20 Commented by mohammad17 last updated on 20/Sep/20 $${help}\:{me}\:{sir} \\ $$ Answered by bobhans last updated on…
Question Number 114656 by vylollloll last updated on 20/Sep/20 $$\mathrm{2}{tanx}−\mathrm{1}=\mathrm{1} \\ $$$$\Leftrightarrow\mathrm{2}{tanx}=\mathrm{1}+\mathrm{1} \\ $$$${tanx}=\frac{\mathrm{2}}{\mathrm{2}}=\mathrm{1} \\ $$ Commented by vylollloll last updated on 20/Sep/20 Commented by…
Question Number 114654 by mohammad17 last updated on 20/Sep/20 Commented by mohammad17 last updated on 20/Sep/20 $${help}\:{me}\:{sir} \\ $$ Commented by mohammad17 last updated on…
Question Number 49116 by hassentimol last updated on 03/Dec/18 $$\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{for}\:: \\ $$$$\mathrm{2}\:=\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\:\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\:\mathrm{2}\:…\:}}}}} \\ $$ Commented by maxmathsup by imad last updated on 03/Dec/18 $${let}\:{u}_{{n}+\mathrm{1}} =\sqrt{\mathrm{2}+{u}_{{n}}…
Question Number 114647 by ZiYangLee last updated on 20/Sep/20 Commented by ZiYangLee last updated on 20/Sep/20 $$<\mathrm{1}+<\mathrm{2}+<\mathrm{3}+<\mathrm{4}+<\mathrm{5}+<\mathrm{6}+<\mathrm{7}=? \\ $$ Commented by ARVIND990 last updated on…