Question Number 126161 by TheMexicanTacosG last updated on 17/Dec/20 $${find}\:\:“{a}'' \\ $$$$ \\ $$$$\:^{{a}} \sqrt{{a}^{\mathrm{2}} \:}\:=\:\left(\left(\mathrm{4}^{−\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{−\mathrm{2}} \:\:\:\:\: \\ $$ Answered by Olaf last…
Question Number 191675 by MATHEMATICSAM last updated on 28/Apr/23 $$\mathrm{Solve}\:\mathrm{for}\:{x}\:: \\ $$$$\left({x}\:−\:\frac{\mathrm{1}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\:\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:=\:{x} \\ $$ Commented by mehdee42 last updated on 29/Apr/23 $${the}\:{graph}\:{of}\:{the}\:{function}\:{is}\:{as}\:{follows}.{therefore}\:.{the}\:{given}\:\: \\…
Question Number 191663 by mathlove last updated on 28/Apr/23 $$\mathrm{2}^{{a}} +\mathrm{4}^{{b}} +\mathrm{8}^{{c}} =\mathrm{328} \\ $$$${find}\:{a},{b}\:{and}\:{c} \\ $$$${when}\left({a},{b},{c}\right){is}\:{natual}\:{number} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 126109 by mnjuly1970 last updated on 17/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:{calculus}… \\ $$$$\:\:{verify}\:\:{that}\:::\:\:\mathrm{A}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}}}{\mathrm{1}+\sqrt{\mathrm{5}}}\:{is} \\ $$$$\:\:\:\:\:\:{a}\:\:{rational}\:\:{number}\:… \\ $$ Answered by som(math1967) last updated on 17/Dec/20 $$\frac{\sqrt[{\mathrm{3}}]{\mathrm{8}\left(\mathrm{2}+\sqrt{\left.\mathrm{5}\right)}\right.}}{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)×\mathrm{2}} \\…
Question Number 126104 by Mathgreat last updated on 17/Dec/20 $$\frac{{a}+{b}}{{c}}\:+\:\frac{{b}+{c}}{{a}}\:+\frac{{a}+{c}}{{b}}\:\geqslant\:\mathrm{4}{a}−\mathrm{3}{b}+{c} \\ $$$${a}\geqslant{b}\geqslant{c} \\ $$ Commented by Mathgreat last updated on 17/Dec/20 $$\boldsymbol{{prove}} \\ $$ Terms…
Question Number 126105 by Mathgreat last updated on 17/Dec/20 $$\mathrm{1}\leqslant{a};{b};{c};{d}\leqslant\mathrm{2} \\ $$$$\mid\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)\left(\mathrm{1}−{c}\right)\left(\mathrm{1}−{d}\right)\mid\leqslant\frac{{abcd}}{\mathrm{4}} \\ $$ Commented by Mathgreat last updated on 17/Dec/20 $$\boldsymbol{{prove}} \\ $$ Answered…
Question Number 191632 by Spillover last updated on 27/Apr/23 $$\int_{\mathrm{0}} ^{\infty} \sqrt{\mathrm{tan}\:\theta}\:{d}\theta \\ $$ Commented by Tinku Tara last updated on 28/Apr/23 $$\mathrm{Q113706} \\ $$…
Question Number 191631 by Spillover last updated on 27/Apr/23 $$\int_{\mathrm{0}} ^{\infty} {x}^{\frac{\mathrm{1}}{\mathrm{2}}} {e}^{−{x}^{\mathrm{2}} } {dx} \\ $$ Answered by malwan last updated on 28/Apr/23 $${put}\:{x}^{\mathrm{2}}…
Question Number 191624 by Shrinava last updated on 27/Apr/23 Answered by ARUNG_Brandon_MBU last updated on 28/Apr/23 $$\int_{\mathrm{1}} ^{{x}} \sqrt{\frac{{t}}{\mathrm{1}+{t}^{\mathrm{3}} }}{dt} \\ $$$$=\int_{\mathrm{1}} ^{{x}} \frac{{t}^{\frac{\mathrm{1}}{\mathrm{2}}} }{\:\sqrt{\mathrm{1}+\left({t}^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 191623 by Shrinava last updated on 27/Apr/23 Answered by mehdee42 last updated on 27/Apr/23 $${let}\::\:{f}\left({x}\right)={ax}+{b} \\ $$$${f}\left({f}\left({x}\right)\right)+{f}\left({x}\right)=−{x}\:\Rightarrow\left({a}^{\mathrm{2}} +{a}\right){x}+{ab}+\mathrm{2}{b}=−{x}\Rightarrow{a}=\frac{−\mathrm{1}+\sqrt{\mathrm{3}}{i}}{\mathrm{2}}={e}^{\frac{\mathrm{2}\pi}{\mathrm{3}}{i}} \:\:\&\:\:{b}=\mathrm{0}\Rightarrow{f}\left({x}\right)={e}^{\frac{\mathrm{2}\pi}{\mathrm{3}}{i}} {x} \\ $$$${f}\left({f}\left({f}\left(\frac{\mathrm{1}}{\mathrm{2}+{cosx}}\right)\right)\right)=\frac{\mathrm{1}}{\mathrm{2}+{cosx}} \\…