Category: Algebra

Question Number 82561 by jagoll last updated on 22/Feb/20 $$apolynomialgivesaremainder$$$$of-x-1whendividedby{x}^{2.}$$$$andaremainderof-1when$$$$dividedbyx-1.whatisthe$$$$remainderwhenthepolynomial$$$$dividedby{x}^2(x-1)?$$ Answered by…

Question Number 17018 by tawa tawa last updated on 29/Jun/17 $$\mathrm{Find}\mathrm{the}\mathrm{cube}\mathrm{root}\mathrm{of}:55+63\sqrt{2}$$ Commented by prakash jain last updated on 29/Jun/17 $${(a+b\sqrt{2})}^3=55+63\sqrt{2}$$$${a}^{\mathrm{3}}…

Question Number 148077 by mathdanisur last updated on 25/Jul/21 $$\int \frac{{cos}^{\mathit{n}}x}{sinx}dx=?$$ Answered by Olaf_Thorendsen last updated on 26/Jul/21 $${\mathrm{I}}_n\left(x\right)=\int \frac{{\cos }^{n}x}{\sin x}dx$$$$…

Question Number 82519 by peter frank last updated on 22/Feb/20 Commented by mathmax by abdo last updated on 23/Feb/20 $${A}_{\theta} =\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{{n}} }{cos}\left({n}\theta\right)\:\:=\sum_{{n}=\mathrm{0}}…

Question Number 148043 by mathdanisur last updated on 25/Jul/21 $$\frac{{(2-\sqrt{2})}^8\cdot {(6+4\sqrt{2})}^8}{{(2+\sqrt{2})}^8}=?$$ Answered by iloveisrael last updated on 25/Jul/21 $$\left[\:\frac{\left(\mathrm{2}−\sqrt{\mathrm{2}}\right)\left(\mathrm{6}+\mathrm{4}\sqrt{\mathrm{2}}\right)}{\mathrm{2}+\sqrt{\mathrm{2}}}\:\right]^{\mathrm{8}} \: \…