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AlgebraQuestion and Answers: Page 264
Question Number 86903 Answers: 0 Comments: 0
Question Number 86825 Answers: 1 Comments: 1
$${a}^{\mathrm{3}} +\frac{\mathrm{1}}{{a}^{\mathrm{3}} }=\mathrm{18} \\ $$$${a}^{\mathrm{4}} +\frac{\mathrm{1}}{{a}^{\mathrm{4}} }=? \\ $$
Question Number 86779 Answers: 1 Comments: 0
$${ssolve} \\ $$$$\left.\mathrm{1}\right){x}−\left[{x}\right]\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right){x}−\left[{x}\right]\leqslant\mathrm{0} \\ $$$$\left.\mathrm{3}\right){x}+\left[{x}\right]\geqslant\mathrm{0} \\ $$$$\left.\mathrm{4}\right){x}+\left[{x}\right]\leqslant\mathrm{0}\: \\ $$
Question Number 86741 Answers: 1 Comments: 4
$$\begin{cases}{{x}+\mathrm{10}{y}+\mathrm{50}{z}=\mathrm{500}}\\{{x}+{y}+{z}=\mathrm{100}}\end{cases} \\ $$$$ \\ $$$${find}\:{x},{y},{z} \\ $$
Question Number 86737 Answers: 2 Comments: 4
$${prove}\:{that} \\ $$$$\mathrm{1}/{cos}\mathrm{2}{x}+{cosx}+\mathrm{1}=\frac{{sin}\frac{\mathrm{5}{x}}{\mathrm{2}}}{\mathrm{2}{sin}\frac{{x}}{\mathrm{2}}}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{2}/\frac{{cos}\left({x}\right)+{isin}\left({x}\right)−\mathrm{1}}{{cos}\left({x}\right)+{isin}\left({x}\right)+\mathrm{1}}=−{i}\:{tan}\left({x}\right) \\ $$$$ \\ $$$$\mathrm{3}/\frac{{cos}\left(\mathrm{5}{x}\right)+{isin}\left(\mathrm{5}{x}\right)+\mathrm{1}}{{cos}\left(\mathrm{5}{x}\right)−{isin}\left({x}\right)+\mathrm{1}}={cos}\left(\mathrm{5}{x}\right)+{isin}\left(\mathrm{5}{x}\right) \\ $$
Question Number 86723 Answers: 0 Comments: 1
Question Number 86610 Answers: 0 Comments: 4
Question Number 86602 Answers: 0 Comments: 0
Question Number 86586 Answers: 1 Comments: 4
Question Number 86541 Answers: 0 Comments: 1
Question Number 86426 Answers: 2 Comments: 0
$${solve}\:{in}\:{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{5}=\left[{x}\right] \\ $$
Question Number 86396 Answers: 0 Comments: 0
Question Number 86298 Answers: 0 Comments: 5
$${let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{2} \\ $$$${x}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}=\pm\sqrt{\mathrm{2}} \\ $$$${then}\:{let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{4} \\ $$$${x}^{\mathrm{4}} =\mathrm{4} \\ $$$${x}=\pm\sqrt[{\mathrm{4}}]{\mathrm{4}}=\pm\sqrt{\mathrm{2}} \\ $$$${so}\:{we}\:{had}\:{prove}\:\mathrm{2}=\mathrm{4}\:{right}? \\ $$
Question Number 86230 Answers: 1 Comments: 0
$${is}\:\:\left(−\mathrm{1}\right)^{\frac{{m}}{{n}}} \:=\left(\sqrt[{{n}}]{\left(−\mathrm{1}\:\right)^{{m}} }\right)\:{or}\:=\left(\sqrt[{{n}}]{−\mathrm{1}}\right)^{{m}} \\ $$$${or}\:{both}\:{of}\:{them}\:{are}\:{fault}\:{and}\:{why}\:? \\ $$
Question Number 86206 Answers: 0 Comments: 3
$$\mathrm{1}.\mathrm{line}:\boldsymbol{\mathrm{y}}=−\boldsymbol{\mathrm{x}}+\mathrm{4}\:\:,\mathrm{meets}\::\:\boldsymbol{\mathrm{xy}}=\mathrm{1}\:\mathrm{at}:\boldsymbol{\mathrm{A}},\boldsymbol{\mathrm{B}}. \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\mathrm{S}_{\mathrm{O}\overset{\bigtriangleup} {\mathrm{A}B}} =?\:\left(\mathrm{O}=\mathrm{origin}\:\mathrm{of}\:\mathrm{cordinates}\right) \\ $$$$\mathrm{2}.\mathrm{find}\::\mathrm{center}\:\mathrm{area}\:\mathrm{of}\:\mathrm{region}\:\mathrm{bonded}\:\mathrm{by} \\ $$$$\mathrm{corve}:\:\:\sqrt{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{a}}}}+\sqrt{\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{b}}}}=\mathrm{1},\mathrm{and}\:\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\:\mathrm{axes}. \\ $$$$\left(\boldsymbol{\mathrm{a}}\neq\boldsymbol{\mathrm{b}}\right)\in\boldsymbol{\mathrm{R}}^{+} \\ $$
Question Number 86141 Answers: 0 Comments: 5
$$\mathrm{A}\:\mathrm{number}\:\mathrm{n}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{of}\:\:\mathrm{22}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{remainder}\:\:\mathrm{30}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{33}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{n} \\ $$
Question Number 86085 Answers: 1 Comments: 4
$$\mathrm{If}\:\mathrm{X}^{\mathrm{2}} +\mathrm{Y}^{\mathrm{2}} =\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{XY}=\mathrm{5} \\ $$$$\mathrm{Find}\:\left(\mathrm{X}^{\mathrm{2}} −\mathrm{Y}^{\mathrm{2}} \right) \\ $$
Question Number 86042 Answers: 3 Comments: 0
$${solve}:\:\:\lfloor\:\sqrt{{x}}\:\rfloor=\lfloor\frac{{x}}{\mathrm{2}}\rfloor \\ $$
Question Number 86009 Answers: 1 Comments: 0
$${solve}\:{in}\:{R}\::\left[\frac{{x}}{\mathrm{2}}\right]+\left[\frac{\mathrm{2}{x}}{\mathrm{3}}\right]−{x}=\mathrm{0} \\ $$
Question Number 86000 Answers: 1 Comments: 0
$${solve}\:{the}\:{equation}\:\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} =\mathrm{4} \\ $$
Question Number 85930 Answers: 0 Comments: 1
Question Number 85902 Answers: 1 Comments: 15
$${find}\:{the}\:{coefficients}\:{of}\:{x}^{\mathrm{2}} \:{and}\:{x}^{\mathrm{3}} \: \\ $$$${terms}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} \left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{3}} ...\left(\mathrm{1}+\mathrm{100}{x}\right)^{\mathrm{100}} \\ $$
Question Number 85871 Answers: 0 Comments: 3
Question Number 85864 Answers: 1 Comments: 0
$${simplify}\:{the}\:{expression} \\ $$$$\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{8}\sqrt{\mathrm{3}}−\mathrm{10}}}\:−\:\sqrt{\mathrm{7}−\sqrt{\mathrm{3}}}\:\:{in} \\ $$$${the}\:{form}\:\sqrt{\sqrt{{a}}+{b}}\:? \\ $$
Question Number 85854 Answers: 0 Comments: 2
$$\mathrm{If}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{4xyz}\:−\mathrm{1}\: \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\: \\ $$
Question Number 85822 Answers: 2 Comments: 1
$$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{3}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{5}}\:=\:\mathrm{0}\: \\ $$
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