Question Number 16542 by gourav~ last updated on 23/Jun/17 $${if}\:\frac{{a}}{\mid{Z}_{\mathrm{2}} −{Z}_{\mathrm{3}} \mid}=\frac{{b}}{\mid{Z}_{\mathrm{3}} −{Z}_{\mathrm{1}} \mid}=\frac{{c}}{\mid{Z}_{\mathrm{1}} −{Z}_{\mathrm{2}} \mid}\:\:{Then}.. \\ $$$${find}..\:\frac{{a}^{\mathrm{2}} }{{Z}_{\mathrm{2}} −{Z}_{\mathrm{3}} }\:+\:\frac{{b}^{\mathrm{2}} }{{Z}_{\mathrm{3}} −{Z}_{\mathrm{1}} }\:+\:\frac{{c}^{\mathrm{2}} }{{Z}_{\mathrm{1}}…
Question Number 147611 by mathdanisur last updated on 22/Jul/21 $$\left(\mathrm{111}\right)_{\mathrm{10}} \:=\:\left({x}\right)_{\mathrm{5}} \\ $$$$\Rightarrow\:{x}\:=\:? \\ $$ Answered by bobhans last updated on 22/Jul/21 $$\left(\mathrm{111}\right)_{\mathrm{10}} =\:\mathrm{1}×\mathrm{10}^{\mathrm{2}} +\mathrm{1}×\mathrm{10}^{\mathrm{1}}…
Question Number 16540 by gourav~ last updated on 23/Jun/17 $${if}\:\mid{Z}\mid=\mathrm{1}\:{Then}\:\frac{\mathrm{1}+{Z}}{\mathrm{1}+\bar {{Z}}}\:\:{is}\:{equal}\:{to}… \\ $$$$\left.{a}\right)\:{Z}\:\: \\ $$$$\left.{b}\right)\:\:\bar {{Z}} \\ $$$$\left.{c}\right)\:{Z}+\bar {{Z}} \\ $$$$\left.{d}\right)\:{N}.{O}.{T} \\ $$ Answered by…
Question Number 82071 by jagoll last updated on 18/Feb/20 $${x}\neq\:{y}\:\neq{z}\:\neq\:\mathrm{0} \\ $$$${xy}\:+\:{xz}\:+\:{yz}\:=\:\mathrm{0} \\ $$$${prove}\:{that}\:\frac{{x}+{y}}{{z}}+\frac{{x}+{z}}{{y}}+\frac{{y}+{z}}{{x}}\:=\:−\mathrm{3} \\ $$$$ \\ $$ Answered by TANMAY PANACEA last updated on…
Question Number 82073 by TawaTawa last updated on 18/Feb/20 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\mathrm{j}_{\mathrm{3}/\mathrm{2}} \left(\mathrm{x}\right)\:\:=\:\:\frac{\sqrt{\mathrm{2}}}{\pi\mathrm{x}}\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\:−\:\mathrm{cos}\:\mathrm{x}\right) \\ $$ Commented by jagoll last updated on 18/Feb/20 $${what}\:{is}\:{j}_{\frac{\mathrm{3}}{\mathrm{2}}} ? \\ $$ Commented…
Question Number 16519 by tawa tawa last updated on 23/Jun/17 $$\mathrm{Solve}: \\ $$$$\mid\mathrm{2}\:−\:\mathrm{x}\mid\:−\:\mathrm{2}\:\mid\mathrm{x}\:+\:\mathrm{1}\mid\:<\:\mathrm{1} \\ $$ Answered by ajfour last updated on 23/Jun/17 Commented by ajfour…
Question Number 147587 by mathdanisur last updated on 22/Jul/21 Commented by ajfour last updated on 22/Jul/21 $${what}\:{if}\:{we}\:{replace}\:{the}\:{r}.{h}.{s}.\:{in} \\ $$$${this}\:{question}\:{by}\:\:\mathrm{2}{x}\:? \\ $$ Answered by iloveisrael last…
Question Number 147585 by mathdanisur last updated on 22/Jul/21 Answered by Rasheed.Sindhi last updated on 22/Jul/21 $$\:\:\:{z}={w}+{f}\::\:{whole}\:{number}\:\&\:{fraction}<\mathrm{1} \\ $$$$\:\:\:\:{w}+{f}−\mathrm{2021}{f}=\mathrm{2021} \\ $$$$\:\:\:\:{w}=\mathrm{2021}{f}−{f}+\mathrm{2021} \\ $$$$\:\:\:\:{w}=\mathrm{2020}{f}+\mathrm{2021} \\ $$$${Let}\:{f}=\frac{{p}}{{q}}\:;\:{p}\:\&\:{q}\:{coprime}\:{p}<{q}…
Question Number 147582 by mathdanisur last updated on 22/Jul/21 $${if}\:\:{x};{y};{z}>\mathrm{0}\:\:{prove}\:{that} \\ $$$$\frac{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} }{{xyz}}\:\geqslant\:\mathrm{2}\left(\frac{{x}}{{y}+{z}}\:+\:\frac{{y}}{{z}+{x}}\:+\:\frac{{z}}{{x}+{y}}\right) \\ $$ Answered by mitica last updated on 22/Jul/21 $${m}_{{h}}…
Question Number 82041 by M±th+et£s last updated on 17/Feb/20 $${show}\:{that} \\ $$$$\pi^{{ie}} +\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0} \\ $$ Commented by mr W last updated on 17/Feb/20 $${certainly}\:{it}'{s}\:{not}\:{your}\:{fault}\:{that}\:{it}\:{is} \\…