Category: Algebra

Question Number 188100 by Shrinava last updated on 25/Feb/23 Answered by a.lgnaoui last updated on 25/Feb/23 $$△ADC\measuredangle CDA=x+18;AC=bCD=$$$$\frac{\sin 18}{b}=\frac{\sin (x+18)}{a}\Rightarrow \frac{\mathit{a}}{\mathit{b}}=\frac{\sin (\mathit{x}+18)}{\sin 18}\left(1\right)$$$$△ABCBD=AC=aBC=a+b$$$$\frac{\sin (x+18)}{a+b}=\frac{\sin 18}{a}$$$${a}\left[\mathrm{sin}\:\left({x}+\mathrm{18}\right)−\mathrm{sin}\:\mathrm{18}\right]={b}\mathrm{sin}\:\mathrm{18}…

Question Number 122551 by shaker last updated on 18/Nov/20 Answered by bramlexs22 last updated on 18/Nov/20 $$\:\int\:\frac{\mathrm{4sin}\:^{\mathrm{2}} \mathrm{2}{x}.\mathrm{cos}\:^{\mathrm{2}} \mathrm{2}{x}}{\mathrm{2cos}\:^{\mathrm{2}} {x}}\:{dx}\:=\:\mathrm{2}\int\:\frac{\mathrm{4sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:^{\mathrm{2}} {x}.\mathrm{cos}\:^{\mathrm{2}} \mathrm{2}{x}}{\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx} \…

Question Number 188073 by Shrinava last updated on 25/Feb/23 $$\mathrm{If}\mathrm{x}=\sqrt{\frac{1+\sqrt{5}}{\sqrt{5}-1}}\mathrm{find}{5\mathrm{x}}^2-5\mathrm{x}-1=?$$ Answered by som(math1967) last updated on 25/Feb/23 $$x=\sqrt{\frac{{(\sqrt{5}+1)}^2}{4}}=\frac{\sqrt{5}+1}{2}$$$$\frac{\mathrm{1}}{{x}}=\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}+\mathrm{1}}=\frac{\mathrm{2}\left(\sqrt{\mathrm{5}}−\mathrm{1}\right)}{\mathrm{4}}=\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}} \…

Question Number 57000 by pieroo last updated on 28/Mar/19 $$\mathrm{If}{(\mathrm{x}+2)}^2\mathrm{is}\mathrm{a}\mathrm{factor}\mathrm{of}\mathrm{the}\mathrm{polynomial}$$$$\mathrm{f}\left(\mathrm{x}\right)={\mathrm{mx}}^3+{\mathrm{x}}^2+\mathrm{x}+\mathrm{n},\mathrm{find};$$$$\mathrm{the}\mathrm{values}\mathrm{of}\mathrm{m}\mathrm{and}\mathrm{n}.$$ Commented by maxmathsup by imad last…

Question Number 188069 by mustafazaheen last updated on 25/Feb/23 $$howissolution$$$$\int \sqrt{e^x}\ln \sqrt{e^x}dx=?$$ Commented by 0670322918 last updated on 25/Feb/23 Terms of…