Category: Algebra

Question Number 82041 by M±th+et£s last updated on 17/Feb/20 $$showthat$$$${\pi }^{ie}+\frac{1}{2}=0$$ Commented by mr W last updated on 17/Feb/20 $${certainly}\:{it}'{s}\:{not}\:{your}\:{fault}\:{that}\:{it}\:{is} \…

Question Number 147566 by mathdanisur last updated on 21/Jul/21 $$x^3+3367=2^{\mathit{n}}\Rightarrow x;n=?$$ Answered by Olaf_Thorendsen last updated on 21/Jul/21 $$x^3+3367=2^n$$$$\mathrm{Solution}\:\mathrm{for}\:{x}\in\mathbb{N}.…

Question Number 147557 by mathdanisur last updated on 21/Jul/21 $$Simlify$$$${(\frac{1+\sqrt{x}}{\sqrt{1+x}}-\frac{\sqrt{1+x}}{1+\sqrt{x}})}^2-{(\frac{1-\sqrt{x}}{\sqrt{1+x}}-\frac{\sqrt{1+x}}{1-\sqrt{x}})}^2$$ Answered by Rasheed.Sindhi last updated on 21/Jul/21 $$\left(\underset{{a}} {\underbrace{\frac{\mathrm{1}+\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}}}\:}}−\:\frac{\sqrt{\mathrm{1}+{x}}}{\mathrm{1}+\sqrt{{x}}}\right)^{\mathrm{2}} -\:\left(\underset{{b}}…

Question Number 147529 by mathdanisur last updated on 21/Jul/21 $$if{a}_{\mathit{n}+1}=\sqrt{a_1+a_{\mathit{n}}}$$$$\text{Double subscripts: use braces to clarify}$$ Commented by mathdanisur last updated on…

Question Number 147488 by mathdanisur last updated on 21/Jul/21 $$ifx;y;z⩾1then:$$$$\frac{1}{3xy-1}+\frac{1}{3yz-1}+\frac{1}{3zx-1}⩾\frac{3}{2xyz}$$ Answered by mindispower last updated on 21/Jul/21 $$infirt$$$$\mathrm{1}\leqslant{xy},{xy}=\frac{{xyz}}{{z}} \…