Question Number 147134 by mathdanisur last updated on 18/Jul/21 $$\sqrt{\mathrm{2}{sin}\left({x}\right)−\mathrm{1}}\:\centerdot\:{sin}\left({x}\right)\:>\:\mathrm{0} \\ $$ Commented by hknkrc46 last updated on 18/Jul/21 $$\blacktriangleright\:\mathrm{2sin}\:\boldsymbol{{x}}\:−\:\mathrm{1}\:>\:\mathrm{0}\:\:\wedge\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\frac{\mathrm{1}}{\mathrm{2}}\:\wedge\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\mathrm{0}\:\equiv\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\blacktriangleright\:\frac{\boldsymbol{\pi}}{\mathrm{6}}\:<\:\boldsymbol{{x}}\:<\:\frac{\mathrm{5}\boldsymbol{\pi}}{\mathrm{6}}\:\: \\…
Question Number 147122 by mathdanisur last updated on 18/Jul/21 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {{lim}}\:\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\mathrm{2}^{\boldsymbol{{k}}} \centerdot\left(\sqrt[{\mathrm{2}^{\boldsymbol{{k}}} }]{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} \:=\:?\: \\ $$ Answered by Kamel last updated on 18/Jul/21…
Question Number 147116 by Rasheed.Sindhi last updated on 18/Jul/21 $${a}+{b}+{c}=\mathrm{1} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{1} \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{1} \\ $$$${a}\:,\:{b}\:,\:{c}\:=? \\ $$ Commented…
Question Number 16047 by vpawarksp@gmail.com last updated on 17/Jun/17 $${number}\:{of}\:{real}\:{solution}\:{of}\:{equation}\:\:\:\:{a}^{\mathrm{2008}} \:+\:\:{b}^{\mathrm{2008}} \:\:=\:\mathrm{2008}{ab}−\mathrm{2006}\:\:\:\:\:\:\:\:\: \\ $$ Commented by Tinkutara last updated on 17/Jun/17 $$\mathrm{You}\:\mathrm{can}\:\mathrm{verify}\:\mathrm{that}\:{a}\:=\:{b}\:=\:\mathrm{1}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{equation}. \\…
Question Number 147119 by mathdanisur last updated on 18/Jul/21 $${if}\:\:\:{x}>−\mathrm{1}\:,\:{q}\geqslant\mathrm{2}\:\:\:{then}: \\ $$$$\left(\mathrm{1}+{x}\right)^{\boldsymbol{{q}}} \:\geqslant\:\mathrm{1}+{qx}+\left({q}−\mathrm{1}\right){x}^{\mathrm{2}} \\ $$ Answered by mindispower last updated on 18/Jul/21 $$ \\ $$$$\mathrm{1}+{qx}+\left({q}−\mathrm{1}\right){x}^{\mathrm{2}}…
Question Number 16029 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 17/Jun/17 Commented by mrW1 last updated on 17/Jun/17 $$\mathrm{no}\:\mathrm{unique}\:\mathrm{solution}. \\ $$$$\begin{vmatrix}{\mathrm{1}}&{−\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}&{−\mathrm{1}}\\{−\mathrm{1}}&{\mathrm{0}}&{\mathrm{1}}\end{vmatrix}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{with}\:\mathrm{p}+\mathrm{q}+\mathrm{r}=\mathrm{0}\:\mathrm{there}\:\mathrm{are}\:\infty\:\mathrm{solutions}. \\ $$$$\mathrm{x}=\mathrm{any}\:\mathrm{value}\:\mathrm{s}…
Question Number 147103 by mnjuly1970 last updated on 18/Jul/21 Answered by mr W last updated on 18/Jul/21 $${x}={n}+{f},\:{n}\in{Z},\:\mathrm{0}\leqslant{f}<\mathrm{1} \\ $$$${x}^{\mathrm{2}} =\left({n}+{f}\right)^{\mathrm{2}} ={n}^{\mathrm{2}} +{f}^{\mathrm{2}} +\mathrm{2}{nf} \\…
Question Number 81552 by ajfour last updated on 14/Feb/20 Commented by jagoll last updated on 14/Feb/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{z}\:?? \\ $$ Commented by jagoll last updated on…
Question Number 16000 by tawa tawa last updated on 16/Jun/17 Answered by mrW1 last updated on 16/Jun/17 $$\mathrm{I}\:\mathrm{assume}\:\mathrm{you}\:\mathrm{mean}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{roots}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{tan}\:\theta\:+\:\mathrm{b}\:\mathrm{sec}\:\theta\:=\:\mathrm{c} \\ $$$$ \\ $$$$\mathrm{a}\:\mathrm{tan}\:\theta\:+\:\mathrm{b}\:\mathrm{sec}\:\theta\:=\:\mathrm{c} \\…
Question Number 147076 by mathdanisur last updated on 17/Jul/21 $${a}+{b}+{c}=\mathrm{1} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{1}\:\:\:\:\:\Rightarrow\:\:\:{abc}=? \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{1} \\ $$ Answered by gsk2684…