Question Number 37568 by math khazana by abdo last updated on 15/Jun/18 $${let}\:\alpha\:{and}\:\beta\:{the}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} \:−\mathrm{2}{mx}\:−\mathrm{1}\:=\mathrm{0}\:\:{find}\:{interms}\:{of}\:{the}\:{real}\:{m} \\ $$$${A}\:=\:\alpha^{\mathrm{2}} \:+\beta^{\mathrm{2}} \\ $$$${B}\:=\alpha^{\mathrm{3}} \:+\beta^{\mathrm{3}} \\ $$$${c}\:=\alpha^{\mathrm{4}} \:+\beta^{\mathrm{4}}…
Question Number 168642 by Shrinava last updated on 15/Apr/22 $$\mathrm{Let}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with} \\ $$$$\angle\mathrm{ABC}=\mathrm{60}°\:\:\mathrm{and}\:\:\angle\mathrm{ACB}=\mathrm{50}°. \\ $$$$\mathrm{IABI}=\mathrm{a}^{\mathrm{2}} −\mathrm{2}\:,\:\mathrm{IBCI}=\mathrm{a}\:\:\mathrm{in}\:\mathrm{this} \\ $$$$\mathrm{instance}\:,\:\mathrm{prove}\:\mathrm{that}\:\:\mathrm{IACI}=\sqrt{\mathrm{3}}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 103094 by I want to learn more last updated on 12/Jul/20 $$. \\ $$ Commented by I want to learn more last updated…
Question Number 103093 by mr W last updated on 12/Jul/20 $${solve}\:{for}\:{x},{y}\in\mathbb{N} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{3}}{\mathrm{202}} \\ $$ Answered by 1549442205 last updated on 13/Jul/20 $$\mathrm{We}\:\mathrm{have}\:\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}=\frac{\mathrm{3}}{\mathrm{202}}\Leftrightarrow\frac{\mathrm{x}+\mathrm{y}}{\mathrm{xy}}=\frac{\mathrm{3}}{\mathrm{202}} \\ $$$$\Leftrightarrow\mathrm{3xy}=\mathrm{202}\left(\mathrm{x}+\mathrm{y}\right)\Leftrightarrow\mathrm{9xy}=\mathrm{3}.\mathrm{202}\left(\mathrm{x}+\mathrm{y}\right)…
Question Number 168606 by Shrinava last updated on 14/Apr/22 Commented by mr W last updated on 14/Apr/22 $$\left[{ABC}\right]={area}\:{of}\:\Delta{ABC}? \\ $$$${is}\:{I}_{{a}} \:{opposite}\:{to}\:{A}? \\ $$ Commented by…
Question Number 168579 by alf123 last updated on 13/Apr/22 Commented by MJS_new last updated on 14/Apr/22 $${y}=\frac{−{x}^{\mathrm{3}} +\mathrm{15}{x}^{\mathrm{2}} −\mathrm{49}{x}−\mathrm{54}}{{x}+\mathrm{1}} \\ $$$$−\infty<{y}<+\infty \\ $$$$\Rightarrow\:\mathrm{no}\:\mathrm{absolute}\:\mathrm{min}/\mathrm{max}\:\mathrm{exist} \\ $$$$\mathrm{for}\:\mathrm{local}\:\mathrm{min}/\mathrm{max}\:\mathrm{solve}\:{y}'=\mathrm{0}…
Question Number 168550 by Shirnivak last updated on 13/Apr/22 Answered by mr W last updated on 13/Apr/22 Commented by mr W last updated on 13/Apr/22…
Question Number 37464 by bholachaudhary211@gamil.com last updated on 13/Jun/18 $$\mathrm{36}\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{2}} -\mathrm{42}\boldsymbol{{x}}^{\mathrm{3}} \boldsymbol{{y}}^{\mathrm{3}} +\mathrm{24}\boldsymbol{{x}}^{\mathrm{5}} \boldsymbol{{y}}^{\mathrm{4}} \\ $$ Commented by Joel579 last updated on 14/Jun/18 $$\mathrm{simplifying}?…
Question Number 168515 by cortano1 last updated on 12/Apr/22 $$\:\:\:\:\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{9}}{\mathrm{3}}\mid+\frac{{x}−\mathrm{3}}{\mathrm{3}}\:>\mathrm{9}\: \\ $$$$\:\:\:\:{x}=? \\ $$ Commented by benhamimed last updated on 12/Apr/22 $$\begin{cases}{\left.{x}^{\mathrm{2}} \left.+{x}−\mathrm{39}>\mathrm{0}\:\:\:\:{si}\:{x}\in\right]−\infty;−\mathrm{3}\right]\cup\left[\mathrm{3};+\infty\left[\right.\right.}\\{−{x}^{\mathrm{2}} +{x}−\mathrm{21}>\mathrm{0}\:\:{si}\:\:{x}\in\left[−\mathrm{3};\mathrm{3}\right]}\end{cases}…
Question Number 102975 by Rio Michael last updated on 12/Jul/20 $$\mathrm{A}\:\mathrm{student}\:\mathrm{can}\:\mathrm{recall}\:\mathrm{6}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{a}\:\mathrm{9}\:\mathrm{digit}\:\mathrm{number}. \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{he}\:\mathrm{get}\:\mathrm{the}\:\mathrm{complete}\:\mathrm{number}? \\ $$ Commented by Rio Michael last updated on 12/Jul/20 $$\mathrm{yes}\:\mathrm{sir}\:\mathrm{am}\:\mathrm{sure}. \\…