Question Number 128712 by Study last updated on 09/Jan/21 $${if}\:{P}\left({x}−\mathrm{1}\right)=\mathrm{2}{x}^{\mathrm{3}} \centerdot{Q}\left({x}\right)+{x}^{\mathrm{2}} \\ $$$${find}\:\frac{{P}\left(\mathrm{1}\right)−\mathrm{4}}{{Q}\left({x}\right)}=?? \\ $$ Commented by Adel last updated on 13/Jan/21 $$\mathrm{p}\left(\mathrm{1}\right)=\boldsymbol{\mathrm{p}}\left(\mathrm{2}−\mathrm{1}\right)=\mathrm{2}×\mathrm{2}^{\mathrm{3}} ×\boldsymbol{\mathrm{Q}}\left(\mathrm{x}\right)+\mathrm{2}^{\mathrm{2}} \\…
Question Number 63175 by Tawa1 last updated on 30/Jun/19 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \:=\:\:\mathrm{16} \\ $$$$\mathrm{x}\:=\:\mathrm{2},\:\:\:\:\:\mathrm{but}\:\mathrm{how}\:\mathrm{to}\:\mathrm{use}\:\mathrm{Lambert}\:\mathrm{W}\:\mathrm{function} \\ $$ Commented by mr W last updated on 30/Jun/19 $${i}\:{remember}\:{you}\:{have}\:{asked}\:{the}\:{same}…
Question Number 63162 by Rio Michael last updated on 29/Jun/19 $${Find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{x}\:{which}\:{satisfy}\:{the}\:{inequalities}\: \\ $$$$\frac{\mathrm{2}}{{x}−\mathrm{1}}\leqslant\frac{\mathrm{1}}{{x}}\:\:{and}\:\:{x}^{\mathrm{2}} −\mid\mathrm{3}{x}\mid+\mathrm{2}<\mathrm{0} \\ $$ Commented by Prithwish sen last updated on 30/Jun/19 $$\frac{\mathrm{2}}{\mathrm{x}−\mathrm{1}}\leqslant\frac{\mathrm{1}}{\mathrm{x}}\:\Rightarrow\mathrm{x}\leqslant−\mathrm{1}…
Question Number 128698 by I want to learn more last updated on 09/Jan/21 Commented by I want to learn more last updated on 09/Jan/21 $$\mathrm{Altitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}.…
Question Number 128684 by Study last updated on 09/Jan/21 $${how}\:{we}\:{can}\:{convert}\:\mathrm{0}.\overset{−} {\mathrm{9}}\:{to}\:\frac{{q}}{{p}}? \\ $$ Answered by liberty last updated on 09/Jan/21 $$\:\mathrm{let}\:\mathrm{r}\:=\:\mathrm{0},\mathrm{99999999999}… \\ $$$$\:\:\:\:\:\:\:\mathrm{10r}\:=\:\mathrm{9}.\mathrm{9999999999}… \\ $$$$\mathrm{substract}\:\Rightarrow\:\mathrm{9r}\:=\:\mathrm{9}\:\Rightarrow\:\mathrm{r}\:=\:\mathrm{1}\:=\:\frac{\mathrm{1}}{\mathrm{1}}\:=\:\frac{\mathrm{2}}{\mathrm{2}}=\frac{\mathrm{n}}{\mathrm{n}}\:;\:\mathrm{n}\neq\:\mathrm{0}…
Question Number 128636 by john_santu last updated on 09/Jan/21 $$\mathrm{Solve}\:\mathrm{diopthantine}\:\mathrm{equation}\: \\ $$$$\:\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}\:=\:\frac{\mathrm{2}}{\mathrm{17}}. \\ $$ Answered by liberty last updated on 09/Jan/21 $$\Rightarrow\:\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}=\frac{\mathrm{2}}{\mathrm{17}}\:;\:\mathrm{2ab}\:=\:\mathrm{17}\left(\mathrm{a}+\mathrm{b}\right) \\ $$$$\mathrm{consider}\:\left(\mathrm{2a}−\mathrm{17}\right)\left(\mathrm{2b}−\mathrm{17}\right)=\mathrm{4ab}−\mathrm{34}\left(\mathrm{a}+\mathrm{b}\right)+\mathrm{17}^{\mathrm{2}} \\…
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Question Number 63095 by aliesam last updated on 28/Jun/19 Answered by MJS last updated on 29/Jun/19 $$\sqrt[{\mathrm{3}}]{\mathrm{4}{x}^{\mathrm{4}} −\mathrm{40}{x}^{\mathrm{2}} +\mathrm{100}}−\sqrt[{\mathrm{3}}]{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{10}}=\mathrm{20}−\mathrm{2}{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} ={s} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{4}{s}^{\mathrm{2}}…
Question Number 63090 by ajfour last updated on 28/Jun/19 $${s}=\sqrt{{a}^{\mathrm{2}} +\left({a}^{\mathrm{2}} −{d}\right)^{\mathrm{2}} }+\sqrt{\left({b}−{a}\right)^{\mathrm{2}} +\left({b}^{\mathrm{2}} −{a}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\sqrt{{b}^{\mathrm{2}} +\left({c}−{b}^{\mathrm{2}} \right)^{\mathrm{2}} }+{c}−{d} \\ $$$$\:{p}=\:{a}\left({a}^{\mathrm{2}} −{d}\right)+\left({a}+{b}\right)\left({b}^{\mathrm{2}}…
Question Number 128617 by ajfour last updated on 08/Jan/21 Commented by ajfour last updated on 08/Jan/21 $${Express}\:{x}\:{in}\:{terms}\:{of}\:{t},\:{then} \\ $$$${use}\:{it}\:{to}\:{solve}\:{x}^{\mathrm{3}} ={x}+{c}. \\ $$ Answered by ajfour…