Category: Algebra

Question Number 79340 by TawaTawa last updated on 24/Jan/20 Commented by john santu last updated on 24/Jan/20 $$letthisnumber:a,ar,{ar}^2$$$$\left(i\right)a\left(\frac{r^3-1}{r-1}\right)=p\Rightarrow \frac{r^3-1}{r-1}=\frac{p}{a}$$$${r}^{\mathrm{2}} +{r}+\mathrm{1}=\frac{{p}}{{a}}\:…

Question Number 144869 by mathdanisur last updated on 29/Jun/21 $$if{3}^{\mathit{z}}=\frac{1}{3^{5\sqrt{3}}\cdot 3^2}find\mathit{z}=?$$ Answered by liberty last updated on 30/Jun/21 $$\:\mathrm{3}^{\mathrm{z}} \:=\:\mathrm{3}^{−\left(\mathrm{2}+\mathrm{5}\sqrt{\mathrm{3}}\right)} \:\Rightarrow\mathrm{z}=−\mathrm{2}−\mathrm{5}\sqrt{\mathrm{3}}…

Question Number 144839 by mathdanisur last updated on 29/Jun/21 $$Ifx=\sqrt[3]{5}+3andy=4\sqrt[3]{3}$$$$Provethat:x-y<0$$ Answered by ajfour last updated on 29/Jun/21 $${(x-3)}^3=5$$$${y}^{\mathrm{3}}…

Question Number 144831 by mathdanisur last updated on 29/Jun/21 $$\frac{3}{1\cdot 2\cdot 3}+\frac{5}{2\cdot 3\cdot 4}+\frac{7}{3\cdot 4\cdot 5}+\frac{9}{4\cdot 5\cdot 6}+\dots \mathrm{\infty }=?$$ Answered by Dwaipayan Shikari last updated on 29/Jun/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2}{n}+\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)}+\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}…

Question Number 144826 by mathdanisur last updated on 29/Jun/21 Answered by mindispower last updated on 29/Jun/21 $${sin}^{-}\left(a\right)+{sin}^{-}\left(b\right)=u$$$$a,b\in [0,1]$$$${sin}\left({u}\right)={a}\sqrt{\mathrm{1}−{b}^{\mathrm{2}} }+{b}\sqrt{\mathrm{1}−{a}^{\mathrm{2}} }…