Question Number 52086 by prakash jain last updated on 03/Jan/19 $$\mathrm{If}\:\mathrm{1},{a}_{\mathrm{1},} {a}_{\mathrm{2}} ,…,{a}_{{n}−\mathrm{1}} \:\mathrm{are}\:{n}^{{th}} \:\mathrm{roots}\:\mathrm{of} \\ $$$$\mathrm{unity},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}. \\ $$$$\left(\mathrm{1}+{a}_{\mathrm{1}} \right)\left(\mathrm{1}+{a}_{\mathrm{2}} \right)..\left(\mathrm{1}+{a}_{{n}−\mathrm{1}} \right)= \\ $$$${n}\:\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{even} \\…
Question Number 117603 by Ar Brandon last updated on 12/Oct/20 $$\mathrm{Let}\:\mathrm{f}\::\:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{function}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{following}\:: \\ $$$$\left(\mathrm{a}\right)\:{f}\left(−{x}\right)=−{f}\left({x}\right) \\ $$$$\left(\mathrm{b}\right)\:{f}\left({x}+\mathrm{1}\right)={f}\left({x}\right)+\mathrm{1} \\ $$$$\left(\mathrm{c}\right)\:{f}\left(\frac{\mathrm{1}}{{x}}\right)=\frac{{f}\left({x}\right)}{{x}^{\mathrm{2}} }\:\mathrm{for}\:\mathrm{all}\:{x}\neq\mathrm{0} \\ $$$$\mathrm{Show}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right){f}\left({x}\right)={x}\:\mathrm{for}\:\mathrm{all}\:{x},\mathrm{y}\in\mathbb{R} \\ $$$$\left(\mathrm{ii}\right)\:{f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left(\mathrm{y}\right)\:\mathrm{for}\:\mathrm{all}\:{x},\mathrm{y}\in\mathbb{R} \\…
Question Number 183120 by Shrinava last updated on 20/Dec/22 $$\mathrm{I}−\mathrm{Incenter}\:\mathrm{in}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\mathrm{A}\left(\mathrm{2},\mathrm{2}\right)\:,\:\mathrm{B}\left(\mathrm{6},\mathrm{4}\right)\:,\:\mathrm{C}\left(\mathrm{4},\mathrm{8}\right)\:,\:\mathrm{M}\left(\mathrm{8},\mathrm{6}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{MI}\:=\:? \\ $$ Answered by manolex last updated on 21/Dec/22 $$\mathbb{I}=\frac{{Aa}+\boldsymbol{{B}}{b}+{Cc}}{{a}+{b}+{c}} \\…
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Question Number 117555 by dw last updated on 12/Oct/20 $${Alternative}\:{forms} \\ $$$$\begin{cases}{\sqrt{{x}}+\sqrt{{y}}=\frac{\mathrm{23}}{\mathrm{12}}}\\{\mathrm{9}{x}+\mathrm{16}{y}=\mathrm{29}}\end{cases} \\ $$$$ \\ $$ Answered by Olaf last updated on 12/Oct/20 $$\sqrt{{y}}\:=\:\frac{\mathrm{23}}{\mathrm{12}}−\sqrt{{x}} \\…
Question Number 183084 by Rasheed.Sindhi last updated on 19/Dec/22 Commented by JDamian last updated on 19/Dec/22 $${Same}\:{Q}\mathrm{182973} \\ $$$${In}\:{fact}\:{you}\:{wrote}\:{down}\:{the}\:{solution} \\ $$ Commented by Rasheed.Sindhi last…
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Question Number 183076 by Engr_Jidda last updated on 19/Dec/22 Answered by TheSupreme last updated on 21/Dec/22 $${t}\:=\:{tan}\left({x}\right) \\ $$$$\mathrm{10}\geqslant{t}\geqslant\frac{\mathrm{7}}{\mathrm{3}} \\ $$$$\left({t}−\mathrm{2}\right)^{\pi} +\left({t}+\mathrm{5}\right)^{\pi} =\left(\mathrm{3}{t}−\mathrm{7}\right)^{\pi} +\left(\mathrm{10}−{t}\right)^{\pi} \\…
Question Number 52007 by Tawa1 last updated on 02/Jan/19 $$\mathrm{Solve}:\:\:\:\:\:\:\:\:\:\:\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{4}}\right)^{\boldsymbol{\mathrm{log}}_{\mathrm{5}} \mathrm{50}\boldsymbol{\mathrm{x}}} \:\:\:=\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{6}} \\ $$ Answered by MJS last updated on 02/Jan/19 $$\left(\frac{{x}}{\mathrm{4}}\right)^{\mathrm{log}_{\mathrm{5}} \:\mathrm{50}{x}} ={x}^{\mathrm{6}} \\…
Question Number 183078 by Engr_Jidda last updated on 19/Dec/22 Terms of Service Privacy Policy Contact: info@tinkutara.com