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AllQuestion and Answers: Page 439
Question Number 172029 Answers: 1 Comments: 5
$${solve}: \\ $$$${x}^{\mathrm{2}} =\mathrm{2}^{{x}} \\ $$
Question Number 172028 Answers: 1 Comments: 0
$${solve}: \\ $$$$\frac{{log}_{\mathrm{2}} \left(\mathrm{9}−\mathrm{2}^{\left.{x}\right)} \right.}{{log}_{\mathrm{2}} \mathrm{2}^{\left(\mathrm{3}−{x}\right)} }={log}_{\mathrm{2}} \mathrm{2} \\ $$
Question Number 172027 Answers: 1 Comments: 1
$${solve} \\ $$$$\frac{\mathrm{5}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}}=\frac{\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{1}}−\frac{\mathrm{4}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{8}} \\ $$
Question Number 172026 Answers: 1 Comments: 0
$${show}\:{that} \\ $$$${sin}^{\mathrm{2}} \alpha+\left(\mathrm{1}+{cos}\alpha\right)^{\mathrm{2}} =\mathrm{2}\left(\mathrm{1}+{cos}\alpha\right) \\ $$
Question Number 172014 Answers: 0 Comments: 2
$${using}\:{properties}\:{of}\:{determinats} \\ $$$${prove}\:{that} \\ $$$$\left[−{yz}\:\:\:\:\:\:{y}^{\mathrm{2}} +{yz}\:\:\:\:\:\:\:{z}^{\mathrm{2}} +{yz}\right] \\ $$$$\left[{x}^{\mathrm{2}} +{xz}\:\:\:−{xz}\:\:\:\:\:\:\:\:\:\:{z}^{\mathrm{2}} +{xy}\right]\:=\left({xy}+{yz}+{zx}\right)^{\mathrm{2}} \\ $$$$ \\ $$$$\left.\:{x}^{\mathrm{2}} +{xy}\:\:\:\:\:{y}^{\mathrm{2}} +{xy}\:\:\:\:\:\:\:\:−{xy}\right] \\ $$
Question Number 172013 Answers: 1 Comments: 0
$${find}: \\ $$$$\int{xe}^{−{ax}} {ax} \\ $$
Question Number 172012 Answers: 1 Comments: 0
$${find} \\ $$$$\int{e}^{{x}} {sinxdx} \\ $$
Question Number 172011 Answers: 1 Comments: 0
$${find}\:{integrate}: \\ $$$$\int{x}^{\mathrm{2}} {e}^{{x}} {dx} \\ $$
Question Number 172010 Answers: 1 Comments: 0
$${find}\:{integrate}: \\ $$$$\int{xe}^{{x}} {dx} \\ $$
Question Number 172009 Answers: 1 Comments: 0
$${solve}: \\ $$$${if}\:{x}=\mathrm{2017},{y}=\mathrm{2018}\:{and}\:{z}=\mathrm{2019},\: \\ $$$${find}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} −{xy}−{yz}−{zx} \\ $$
Question Number 172008 Answers: 0 Comments: 0
$${solve}: \\ $$$$\mathrm{15}\left(\mathrm{2}{n}\right)_{{C}_{\left({n}−\mathrm{1}\right)} } =\mathrm{28}\left(\mathrm{2}{n}−\mathrm{1}\right)_{{C}_{{n}} } .\:{find}\:{n} \\ $$
Question Number 172007 Answers: 1 Comments: 0
$${solve}: \\ $$$${x}\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:−{x}^{\mathrm{2}} =−\mathrm{6} \\ $$
Question Number 172006 Answers: 1 Comments: 0
$${solve}: \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} +\mathrm{5}\:}\:=\mathrm{1} \\ $$
Question Number 172005 Answers: 2 Comments: 0
$${find}\:{x}:\:\left({log}_{\mathrm{10}} {x}\right)^{\mathrm{2}} −{log}_{\mathrm{10}} {x}=\mathrm{0} \\ $$
Question Number 172023 Answers: 0 Comments: 0
$${if}:\: \\ $$$${bx}^{\mathrm{3}} −\left(\mathrm{3}{b}+\mathrm{2}\right){x}^{\mathrm{2}} −\mathrm{2}\left(\mathrm{5}{b}−\mathrm{3}\right){x}+\mathrm{20}=\mathrm{0} \\ $$$${find}\:{b}\:{in}\:{term}. \\ $$
Question Number 172022 Answers: 1 Comments: 0
$${find}\:{the}\:{cubic}\:{of} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{26}+\mathrm{15}\sqrt{\mathrm{3}}}\:\:\:+\:\sqrt[{\mathrm{3}}]{\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}} \\ $$
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
$${solve}: \\ $$$$\left(\frac{{x}}{\mathrm{12}}\right)^{{log}_{\sqrt{\mathrm{3}}} \:{x}} =\left(\frac{{x}}{\mathrm{18}}\right)^{{log}_{\sqrt{\mathrm{2}}} {x}} \\ $$$$ \\ $$
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