Category: Algebra

Question Number 164196 by HongKing last updated on 15/Jan/22 $$\mathrm{Evalute}\mathrm{the}\mathrm{sum}:$$$$\underset{\mathbf{k}=1}{\sum ^{\mathbf{n}}}\mathrm{k}{\left(\frac{\pi }{\mathrm{n}}\right)}^2\arctan {\left(\frac{\mathrm{k}\pi }{\mathrm{n}}\right)}^2$$ Answered by mathmax by abdo last updated on…

Question Number 164191 by mathlove last updated on 15/Jan/22 Answered by cortano1 last updated on 15/Jan/22 Commented by MJS_new last updated on 15/Jan/22 $$\mathrm{there}'\mathrm{s}\:\mathrm{only}\:\mathrm{1}\:\mathrm{solution}\:\mathrm{and}\:\mathrm{it}'\mathrm{s} \…

Question Number 164156 by HongKing last updated on 14/Jan/22 $$\mathrm{if}\mathrm{ABC}\mathrm{is}\mathrm{a}\mathrm{triangle}\mathrm{with}\mathrm{usual}$$$$\mathrm{notations},\mathrm{then}\mathrm{prove}\mathrm{the}\mathrm{following}$$$$\mathrm{inequality}:$$$${(4\mathrm{R}+\mathrm{r})}^3-{4\mathrm{r}}^2(2\mathrm{R}-\mathrm{r})-{3\mathrm{s}}^2(2\mathrm{R}+\mathrm{r})⩾0$$ Terms of Service Privacy…

Question Number 164154 by HongKing last updated on 14/Jan/22 $$\{\begin{array}{l}{\mathrm{x}}^2+\mathrm{xy}+{\mathrm{y}}^2=9\\ {\mathrm{y}}^2+\mathrm{yz}+{\mathrm{z}}^2=16\\ {\mathrm{x}}^2+\mathrm{xz}+{\mathrm{z}}^2=25\end{array}$$$$\mathrm{Find}:\mathrm{S}=\mathrm{xy}+\mathrm{yz}+\mathrm{xz}$$ Answered by behi834171 last updated…

Question Number 164148 by mathlove last updated on 14/Jan/22 $$ln\left(\frac{3^x}{\frac{27}{81}}\right)=0thenx=?$$ Answered by nikif99 last updated on 14/Jan/22 $$\log {}_{b}1=0\Rightarrow$$$$\left(\frac{\mathrm{3}^{{x}} }{\frac{\mathrm{27}}{\mathrm{81}}}\right)=\mathrm{1}\:\Rightarrow\mathrm{3}^{{x}}…