Question Number 38477 by Sr@2004 last updated on 26/Jun/18 Answered by $@ty@m last updated on 26/Jun/18 $$\frac{{a}−{b}}{{c}}+\frac{{b}−{c}}{{a}}+\frac{{c}+{a}}{{b}}=\mathrm{1} \\ $$$$\Rightarrow\frac{{a}−{b}}{{c}}+\frac{{c}+{a}}{{b}}=\mathrm{1}−\frac{{b}−{c}}{{a}} \\ $$$$\Rightarrow\frac{{b}\left({a}−{b}\right)+{c}\left({c}+{a}\right)}{{bc}}=\frac{{a}−{b}+{c}}{{a}} \\ $$$$\Rightarrow\frac{\left({a}−{b}+{c}\right)\left({b}+{c}\right)}{{bc}}=\frac{{a}−{b}+{c}}{{a}} \\ $$$$\Rightarrow\frac{{b}+{c}}{{bc}}=\frac{\mathrm{1}}{{a}}…
Question Number 169539 by Shrinava last updated on 02/May/22 Commented by mr W last updated on 02/May/22 $$\frac{{R}}{{OI}}=\sqrt{\frac{\mathrm{3}}{\mathrm{2}}}\:? \\ $$ Commented by Shrinava last updated…
Question Number 169533 by cortano1 last updated on 02/May/22 $$\:\:\begin{cases}{{x}+\frac{\mathrm{1}}{{y}}=\mathrm{1}}\\{\frac{\mathrm{1}}{{x}}+{y}=\mathrm{2}}\end{cases}\Rightarrow{x}^{\mathrm{2022}} +\frac{\mathrm{1}}{{y}^{\mathrm{2022}} }\:=? \\ $$ Commented by greougoury555 last updated on 02/May/22 $$\:\:{x}=\frac{{y}−\mathrm{1}}{{y}}\:\wedge\:\frac{{y}}{{y}−\mathrm{1}}+{y}\:=\:\mathrm{2} \\ $$$$\Rightarrow{y}+{y}^{\mathrm{2}} −{y}\:=\:\mathrm{2}{y}−\mathrm{2}…
Question Number 38459 by ajfour last updated on 25/Jun/18 $${x}^{\mathrm{2}} \left({x}−{b}^{\mathrm{2}} \right)+{a}^{\mathrm{2}} {b}^{\mathrm{2}} \left({x}−{a}^{\mathrm{2}} \right)=\mathrm{0} \\ $$$${Solve}\:{for}\:{x}. \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on…
Question Number 103983 by I want to learn more last updated on 18/Jul/20 $$\mathrm{If}\:\:\alpha\:\:\mathrm{and}\:\:\beta\:\:\mathrm{are}\:\mathrm{two}\:\mathrm{unequal}\:\mathrm{angle},\:\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}, \\ $$$$\:\:\:\:\mathrm{a}\:\mathrm{cos}\left(\alpha\right)\:\:+\:\:\mathrm{b}\:\mathrm{sin}\left(\beta\right)\:\:=\:\:\mathrm{c},\:\:\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\:\:\:\mathrm{sin}\left(\frac{\alpha\:\:+\:\beta}{\mathrm{2}}\right)\:\mathrm{sec}\left(\frac{\alpha\:\:−\:\:\beta}{\mathrm{2}}\right)\:\:=\:\:\frac{\mathrm{b}}{\mathrm{c}} \\ $$$$\left(\mathrm{ii}\right)\:\:\:\:\:\mathrm{tan}\left(\frac{\alpha}{\mathrm{2}}\right)\:\mathrm{tan}\left(\frac{\beta}{\mathrm{2}}\right)\:\:=\:\:\frac{\mathrm{c}\:\:−\:\:\mathrm{a}}{\mathrm{c}\:\:+\:\:\mathrm{a}} \\ $$ Terms of Service…
Question Number 103914 by bobhans last updated on 18/Jul/20 $$\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}^{\mathrm{2}} } \:+\:\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{x}^{\mathrm{2}} } \:=\:\mathrm{4}\: \\ $$ Commented by som(math1967) last updated on 18/Jul/20 $$\mathrm{let}\:\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{x}^{\mathrm{2}} }…
Question Number 103921 by Rio Michael last updated on 18/Jul/20 $$\mathrm{Prove}\:\mathrm{that}\:\forall\:{x}\:\in\:\bar {\mathbb{R}}\:,\:\mid\:\mathrm{cos}\:{x}\:\mid\:\leqslant\:\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{2}} \:{x} \\ $$ Answered by Worm_Tail last updated on 18/Jul/20 $${cosx}=\sqrt{\mathrm{1}−{sin}^{\mathrm{2}} {x}\:\:\:\:\:\:\:\:} \\…
Question Number 169445 by infinityaction last updated on 30/Apr/22 $$ \\ $$$$\:\:\:\mathrm{let}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{reals}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{3}} \:+\mathrm{30xy}\:=\:\mathrm{2000} \\ $$$$\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{10} \\ $$ Commented by mr W…
Question Number 169439 by Giantyusuf last updated on 30/Apr/22 Answered by mr W last updated on 30/Apr/22 $${a}^{\mathrm{2}} {x}^{\mathrm{2}} +{a}^{\mathrm{2}} {y}^{\mathrm{2}} +{b}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} {y}^{\mathrm{2}}…
Question Number 169432 by mathlove last updated on 30/Apr/22 $${n}\left({A}\right)=\mathrm{7} \\ $$$${n}\left({A}\cap{B}\right)=\mathrm{4} \\ $$$$\mathrm{3}{n}\left({A}−{B}\right)={n}\left({B}\right) \\ $$$${n}\left({B}−{A}\right)=? \\ $$ Answered by blackmamba last updated on 30/Apr/22…