Question Number 152544 by liberty last updated on 29/Aug/21 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{real}\:\mathrm{zeros}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\:\mathrm{P}_{\mathrm{a}} \left(\mathrm{x}\right)=\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{ax}^{\mathrm{2}} \\ $$$$\mathrm{where}\:\mathrm{a}\:\mathrm{is}\:\mathrm{a}\:\mathrm{given}\:\mathrm{real}\:\mathrm{number} \\ $$ Commented by MJS_new last updated on…
Question Number 21464 by mondodotto@gmail.com last updated on 24/Sep/17 Answered by myintkhaing last updated on 24/Sep/17 $$\mathrm{y}+\delta\mathrm{y}=\sqrt{\mathrm{tan}\left(\mathrm{x}+\delta\mathrm{x}\right)} \\ $$$$\delta\mathrm{y}=\sqrt{\mathrm{tan}\left(\mathrm{x}+\delta\mathrm{x}\right)}−\sqrt{\mathrm{tanx}} \\ $$$$\:\:\:\:\:=\left(\sqrt{\mathrm{tan}\left(\mathrm{x}+\delta\mathrm{x}\right)}−\sqrt{\mathrm{tanx}}\right)\frac{\sqrt{\mathrm{tan}\left(\mathrm{x}+\delta\mathrm{x}\right)}+\sqrt{\mathrm{tanx}}}{\:\sqrt{\mathrm{tan}\left(\mathrm{x}+\delta\mathrm{x}\right)}+\sqrt{\mathrm{tanx}}} \\ $$$$\:\:\:\:\:=\frac{\mathrm{tan}\left(\mathrm{x}+\delta\mathrm{x}\right)−\mathrm{tanx}}{\:\sqrt{\mathrm{tan}\left(\mathrm{x}+\delta\mathrm{x}\right)}+\sqrt{\mathrm{tanx}}}=\frac{\frac{\mathrm{tanx}+\mathrm{tan}\delta\mathrm{x}}{\mathrm{1}−\mathrm{tanxtan}\delta\mathrm{x}}−\mathrm{tanx}}{\mathrm{tan}\sqrt{\left(\mathrm{x}+\delta\mathrm{x}\right)}+\sqrt{\mathrm{tanx}}} \\ $$$$=\frac{\mathrm{tan}\delta\mathrm{x}\left(\mathrm{1}+\mathrm{tan}^{\mathrm{2}}…
Question Number 21459 by x² – y²@gmail.com last updated on 24/Sep/17 $$\mathrm{Solve} \\ $$$$\sqrt{{x}\:+\:\mathrm{1}\:−\:\mathrm{4}\sqrt{{x}\:−\:\mathrm{3}}}\:+\:\sqrt{{x}\:+\:\mathrm{22}\:+\:\mathrm{10}\sqrt{{x}\:−\:\mathrm{3}}}\:=\:\mathrm{7} \\ $$ Answered by Tikufly last updated on 27/Sep/17 $$ \\…
Question Number 86987 by naka3546 last updated on 01/Apr/20 Commented by mr W last updated on 01/Apr/20 $$\Rightarrow\:{Q}\mathrm{86907} \\ $$ Terms of Service Privacy Policy…
Question Number 152513 by ZiYangLee last updated on 29/Aug/21 $$\int\:\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{8}}\:{dx}\:=? \\ $$ Commented by alisiao last updated on 29/Aug/21 $$ \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\:\int\:\frac{{dx}}{\left({x}+\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} +\frac{\mathrm{55}}{\mathrm{16}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\int\:\:\frac{{dt}}{{t}^{\mathrm{2}} +\frac{\mathrm{55}}{\mathrm{16}}}\:…
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Question Number 21426 by x² – y²@gmail.com last updated on 23/Sep/17 $$\mathrm{given}\:\sqrt{\mathrm{2017}{x}^{\mathrm{2}} \:+\:\mathrm{4034}{x}\:+\:\mathrm{17}}\:+\:\sqrt{\mathrm{2017}{x}^{\mathrm{2}} \:+\:\mathrm{4034}{x}\:−\:\mathrm{3}}\:=\:\mathrm{10}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}. \\ $$ Answered by $@ty@m last updated on…
Question Number 86948 by gny last updated on 01/Apr/20 $$\frac{−{sin}\alpha+\mathrm{3}{cos}\alpha}{\mathrm{4}{cos}\alpha+\mathrm{3}{sin}\alpha} \\ $$$$ \\ $$$${tg}\alpha=−\mathrm{3} \\ $$$${pls}\:{help}\:{me}\:{sir} \\ $$ Commented by Prithwish Sen 1 last updated…
Question Number 86946 by A8;15: last updated on 01/Apr/20 Commented by john santu last updated on 01/Apr/20 $$\mathrm{A}^{\mathrm{2}} \:\mathrm{sin}\:^{\mathrm{2}} \mathrm{Ax}\:\:=\:\mathrm{B}^{\mathrm{2}} \:\mathrm{sin}\:\mathrm{Bx}\: \\ $$$$\Rightarrow\mathrm{sin}\:^{\mathrm{2}} \:\mathrm{Ax}\:=\:\frac{\mathrm{B}^{\mathrm{2}} }{\mathrm{A}^{\mathrm{2}}…