Category: Algebra

Question Number 123175 by mathocean1 last updated on 23/Nov/20 $$Showbyrecurrencethat$$$$\mathrm{\forall }n\in \mathbb{N},\sum _{k=0}^{n-1}{q}^k=\frac{q^n-1}{q-1}$$ Answered by PNL last updated on 24/Nov/20…

Question Number 188704 by mathlove last updated on 05/Mar/23 Answered by a.lgnaoui last updated on 05/Mar/23 $$posonsZ=avec:A=x\sqrt{x}-x=x(\sqrt{x}-1)$$$$B=\frac{\sqrt[4]{x^3}-1}{\sqrt[4]{x}-1}-\sqrt{x}C=\frac{\sqrt[4]{x^3}+1}{\sqrt[4]{x}+1}-\sqrt{x}$$$$B=\frac{\sqrt{x}-1}{\sqrt[4]{x}-1}C=\frac{1-\sqrt{x}}{\sqrt[4]{x}+1}B\times C=1-\sqrt{x}$$$$\Rightarrow\:\frac{{A}}{{B}×{C}}=\frac{{x}\left(\sqrt{{x}}\:−\mathrm{1}\right)}{\:\sqrt{{x}}\:−\mathrm{1}}\:\:\:\:…

Question Number 188653 by Shrinava last updated on 04/Mar/23 $$\mathrm{In}\mathrm{how}\mathrm{many}\mathrm{different}\mathrm{ways}\mathrm{can}\mathrm{the}$$$$\mathrm{letters}\mathrm{of}\mathrm{the}\mathrm{word}\mathrm{ABRAKADABRA}$$$$\mathrm{be}\mathrm{arranged}?$$ Commented by Ajetunmobi last updated on 04/Mar/23 $$\frac{\mathrm{11}!}{\mathrm{5}!×\mathrm{2}!×\mathrm{2}!}=\mathrm{83160} \…

Question Number 123114 by nimnim last updated on 23/Nov/20 $$Isthereanysolution\left(s\right)??$$$$\{\begin{array}{l}36x^{2}y-27y^3=8\\ 4x^3-27{xy}^2=4\end{array}$$$$please\dots .$$ Commented by benjo_mathlover last updated…

Question Number 188647 by Rupesh123 last updated on 04/Mar/23 Commented by mr W last updated on 05/Mar/23 $$4.$$$$\underset{{max}} {\mathrm{3}}^{\:\:\:\frac{\mathrm{1}}{\mathrm{3}}} >\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{4}^{\frac{\mathrm{1}}{\mathrm{4}}} >\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{5}}} >\mathrm{6}^{\frac{\mathrm{1}}{\mathrm{6}}}…