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} \\ $$$${f}\left({f}\left({x}\right)\right)+{f}\left({x}\right)=−{x}\:\Rightarrow\left({a}^{\mathrm{2}} +{a}\right){x}+{ab}+\mathrm{2}{b}=−{x}\Rightarrow{a}=\frac{−\mathrm{1}+\sqrt{\mathrm{3}}{i}}{\mathrm{2}}={e}^{\frac{\mathrm{2}\pi}{\mathrm{3}}{i}} \:\:\&\:\:{b}=\mathrm{0}\Rightarrow{f}\left({x}\right)={e}^{\frac{\mathrm{2}\pi}{\mathrm{3}}{i}} {x} \\ $$$${f}\left({f}\left({f}\left(\frac{\mathrm{1}}{\mathrm{2}+{cosx}}\right)\right)\right)=\frac{\mathrm{1}}{\mathrm{2}+{cosx}} \\…
Question Number 191615 by MATHEMATICSAM last updated on 27/Apr/23 $${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{0}.\:\mathrm{Prove}\:\mathrm{that}, \\ $$$$\frac{{a}}{{a}^{\mathrm{2}} \:−\:{bc}}\:+\:\frac{{b}}{{b}^{\mathrm{2}} \:−\:{ca}}\:+\:\frac{{c}}{{c}^{\mathrm{2}} \:−\:{ab}}\:=\:\mathrm{0}. \\ $$ Answered by som(math1967) last updated on 27/Apr/23 $$\:{a}+{b}+{c}=\mathrm{0}…
Question Number 191614 by vishal1234 last updated on 27/Apr/23 $$\frac{\alpha^{\mathrm{100}} +\beta^{\mathrm{100}} }{\alpha^{\mathrm{100}} −\beta^{\mathrm{100}} }\:=\: \\ $$$$\frac{\left(−{w}\right)^{\mathrm{100}} +\left(−{w}^{\mathrm{2}} \right)^{\mathrm{100}} }{\left(−{w}\right)^{\mathrm{100}} −\left(−{w}^{\mathrm{2}} \right)^{\mathrm{100}} } \\ $$$$=\:\frac{{w}^{\mathrm{100}} +{w}^{\mathrm{200}}…