Category: Algebra

Question Number 161930 by Rasheed.Sindhi last updated on 24/Dec/21 $$\{\begin{array}{l}{a}_0=-2\\ a_n=a_{n-1}+2n\end{array};a_n=?$$ Answered by mr W last updated on 24/Dec/21 $${a}_{{n}}…

Question Number 30849 by Penguin last updated on 27/Feb/18 $$x^7+x^6+x^5+x^4+x^3+x^2+x+1=0$$$$$$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{7}} {\sum}}\left[\Re\left({x}_{{k}} \right)\right]^{\mathrm{2}} \:=\:? \…

Question Number 161900 by HongKing last updated on 23/Dec/21 $$0<\mathrm{x};\mathrm{y};\mathrm{z}<1$$$$(1-\mathrm{x})(1-\mathrm{y})(1-\mathrm{z})=\mathrm{xyz}$$$$\mathrm{Find}:$$$$\mathrm{\Omega }=\min (\frac{1-\mathrm{x}}{\mathrm{xy}}+\frac{1-\mathrm{y}}{\mathrm{yz}}+\frac{1-\mathrm{z}}{\mathrm{zx}})$$ Answered by aleks041103 last updated on 24/Dec/21…

Question Number 161884 by HongKing last updated on 23/Dec/21 $$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$$\sqrt[7]{2^{\mathbf{x}}+2^{-1}}=1+\sqrt[7]{2^{\mathbf{x}}-2^{-1}}$$ Commented by mr W last updated on…

Question Number 161868 by cortano last updated on 23/Dec/21 $${\left(\sqrt{2+\sqrt{3}}\right)}^x+\frac{1}{{\left(\sqrt{2+\sqrt{3}}\right)}^x}=2^x$$$$x=?$$ Answered by Rasheed.Sindhi last updated on 23/Dec/21 $${a}=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:,\:\frac{\mathrm{1}}{{a}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}×\frac{\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}}{\:\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}} \…