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Question Number 172021 Answers: 1 Comments: 0
$${solve}: \\ $$$$\mathrm{2}^{{x}^{\mathrm{2}} } ={x}^{\mathrm{2}{x}} \\ $$
Question Number 172024 Answers: 1 Comments: 0
$${let}\:\alpha\:{and}\:\beta\:{be}\:{the}\:{root}\:{of}\:{the}\:{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}.\:{find}\:{the}\:{equation}\:{whose}\:{roots} \\ $$$${are}\:\left(\frac{\mathrm{1}}{\alpha}+\frac{\mathrm{1}}{\beta}\right)\:{and}\:\left(\frac{\mathrm{1}}{\alpha}−\frac{\mathrm{1}}{\beta}\right) \\ $$
Question Number 172002 Answers: 0 Comments: 0
$${if}\:{y}={bcoslog}\left(\frac{{x}}{{n}}\right)^{{n}} ,\:{then} \\ $$$$\frac{{dy}}{{dx}}=? \\ $$
Question Number 172001 Answers: 0 Comments: 0
$${solve}: \\ $$$$\int\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{1}}}{dx} \\ $$
Question Number 172000 Answers: 0 Comments: 0
$${prove}\:{that}: \\ $$$$\frac{{sinx}}{{sin}\mathrm{3}{x}}+\frac{{tanx}}{{tan}\mathrm{3}{x}}=\mathrm{1} \\ $$
Question Number 171999 Answers: 1 Comments: 0
$${resolve}: \\ $$$$\frac{\mathrm{4}\left({x}−\mathrm{4}\right)}{{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}}\:{into}\:{partial}\:{fraction} \\ $$
Question Number 171998 Answers: 0 Comments: 0
$${if} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{81},\:{then}\:{find}\: \\ $$$$\frac{{x}^{\mathrm{6}} +\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{5}{x}} \\ $$
Question Number 172019 Answers: 0 Comments: 0
$${solve}: \\ $$$${x}^{\mathrm{3}} +\mathrm{9}{x}^{\mathrm{2}} {y}=\mathrm{10} \\ $$$${y}^{\mathrm{3}} +{xy}^{\mathrm{2}} =\mathrm{2} \\ $$
Question Number 172025 Answers: 1 Comments: 0
$${find}\:{the}\:{root}\:{of}\: \\ $$$${x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{11}{x}^{\mathrm{2}} +\mathrm{14}{x}−\mathrm{30}=\mathrm{0}. \\ $$
Question Number 171995 Answers: 0 Comments: 0
$${solve}: \\ $$$$\left(\frac{{x}}{\mathrm{12}}\right)^{{log}_{\sqrt{\mathrm{3}}} \:{x}} =\left(\frac{{x}}{\mathrm{18}}\right)^{{log}_{\sqrt{\mathrm{2}}} {x}} \\ $$$$ \\ $$
Question Number 171993 Answers: 0 Comments: 3
Question Number 172020 Answers: 1 Comments: 0
$${solve}: \\ $$$$\mathrm{2}^{{x}} =\mathrm{10}{x} \\ $$
Question Number 171990 Answers: 1 Comments: 0
$${solve}: \\ $$$${log}_{\mathrm{7}} \mathrm{2}\:+\:{log}_{\mathrm{49}} {x}\:={log}_{\mathrm{7}} \sqrt{\mathrm{3}} \\ $$
Question Number 171989 Answers: 1 Comments: 0
$${solve}:\:{A}\:{two}\:{digit}\:{number}\:{is}\:{such} \\ $$$${that}\:\mathrm{4}\:{times}\:{the}\:{unit}\:{digit}\:{is}\:\mathrm{5}\:{more}\: \\ $$$${than}\:{thrice}\:{the}\:{ten}\:{digit}.\:{when}\:{the} \\ $$$${digit}\:{are}\:{reversed}\:{the}\:{number}\:{is}\: \\ $$$${increase}\:{by}\:{nine},\:{find}\:{the}\:{number} \\ $$$$ \\ $$
Question Number 171988 Answers: 0 Comments: 0
$${solve}: \\ $$$${x}^{\mathrm{2}} =\mathrm{16}^{{x}} \\ $$
Question Number 171984 Answers: 0 Comments: 0
Question Number 171979 Answers: 1 Comments: 0
Question Number 171972 Answers: 1 Comments: 0
Question Number 171971 Answers: 2 Comments: 0
$$\int\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{3}}\:{dx}=... \\ $$
Question Number 171966 Answers: 0 Comments: 0
Question Number 171955 Answers: 2 Comments: 0
$$\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)+\:\boldsymbol{{f}}\left(\frac{\mathrm{1}}{\mathrm{1}−\boldsymbol{{x}}}\right)\:=\:\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)} \\ $$$$\:\:\:\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:=\:\:??\:\:\:\:\:\:\:\:\: \\ $$
Question Number 171954 Answers: 0 Comments: 0
$$\mathrm{Find}\:\mathrm{without}\:\mathrm{softs}: \\ $$$$\int_{\frac{\mathrm{1}}{\boldsymbol{\mathrm{e}}}} ^{\:\boldsymbol{\mathrm{e}}} \:\frac{\mathrm{dx}}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}\:+\:\mathrm{x}\:\mathrm{log}^{\mathrm{7}} \:\mathrm{x}\right)} \\ $$
Question Number 171985 Answers: 0 Comments: 0
$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:,\:\mathrm{O}-\mathrm{circumcentr}\:,\:\mathrm{G}-\mathrm{centroid}. \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{OG}\parallel\mathrm{BC}\Leftrightarrow\left(\mathrm{b}^{\mathrm{2}} −\mathrm{c}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{4a}^{\mathrm{2}} \left(\mathrm{9R}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{c}^{\mathrm{2}} \right) \\ $$
Question Number 171944 Answers: 0 Comments: 5
$${if} \\ $$$${a}+{b}+{c}=\mathrm{2196} \\ $$$$\sqrt[{\mathrm{3}}]{{a}}\:+{b}+{c}=\mathrm{2076} \\ $$$${a}+\sqrt[{\mathrm{3}}]{{b}}\:+{c}=\mathrm{1860} \\ $$$${a}+{b}+\sqrt[{\mathrm{3}}]{{c}}\:=\mathrm{480},\:{determine}\:{the}\:{value}\:{of} \\ $$$${a}^{\frac{\mathrm{2}}{\mathrm{3}}} +{b}^{\frac{\mathrm{2}}{\mathrm{3}}} +{c}^{\frac{\mathrm{2}}{\mathrm{3}}} ,\:{if}\:{a},{b},{c}\:{are}\:{all}\:{integer}. \\ $$
Question Number 171941 Answers: 0 Comments: 3
$$\sqrt{{a}}+\sqrt{{b}}=\sqrt{\mathrm{2009}}.\:{find}\:{a}\:{and}\:{b}. \\ $$
Question Number 171930 Answers: 0 Comments: 0
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