Category: Algebra

Question Number 128090 by ajfour last updated on 04/Jan/21 $$someonehelpchekingthis:$$$$x^3=x+c$$$$letx=(p-2q)+(q-2p)$$$$=-(p+q)$$$$p^3-8q^3-6pq(p-2q)+$$$${q}^{\mathrm{3}} −\mathrm{8}{p}^{\mathrm{3}} −\mathrm{6}{pq}\left({q}−\mathrm{2}{p}\right)+…

Question Number 128048 by bramlexs22 last updated on 04/Jan/21 $$\underset{\mathrm{n}=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{\mathrm{n}}}{8\mathrm{n}+3}=?$$ Answered by Olaf last updated on 04/Jan/21 $$\mathrm{L}\left(\lambda,\alpha,{s}\right)\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{e}^{\mathrm{2}{i}\pi\lambda{n}}…

Question Number 62489 by Tawa1 last updated on 21/Jun/19 $$\mathrm{solve}\mathrm{for}\mathrm{x}:\frac{\sqrt{2-\mathrm{x}}+\sqrt{2+\mathrm{x}}}{\sqrt{2-\mathrm{x}}-\sqrt{2+\mathrm{x}}}=3$$ Answered by som(math1967) last updated on 22/Jun/19 $$\frac{\sqrt{2-x}+\sqrt{2+x}+\sqrt{2-x}-\sqrt{2+x}}{\sqrt{2-x}+\sqrt{2+x}-\sqrt{2-x}+\sqrt{2+x}}=\frac{3+1}{3-1}★$$$$\frac{2\sqrt{2-x}}{2\sqrt{2+x}}=\frac{4}{2}$$$$\frac{\mathrm{2}−{x}}{\mathrm{2}+{x}}=\mathrm{4}\:\:\bigstar\bigstar \…

Question Number 62468 by bshahid010@gmail.com last updated on 21/Jun/19 Commented by mathmax by abdo last updated on 21/Jun/19 $$let{3}^x=t\Rightarrow (k-2)t^2-2t+3>0\mathrm{\forall }t>0\Rightarrow {\mathrm{\Delta }}^{{}^{\prime }}<0\Rightarrow$$$$\left(−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{3}\left({k}−\mathrm{2}\right)<\mathrm{0}\:\Rightarrow\mathrm{1}−\mathrm{3}{k}\:+\mathrm{6}\:<\mathrm{0}\:\Rightarrow\mathrm{7}−\mathrm{3}{k}\:<\mathrm{0}\:\Rightarrow{k}>\frac{\mathrm{7}}{\mathrm{3}}…

Question Number 62452 by Tawa1 last updated on 21/Jun/19 $$\mathrm{Find}\mathrm{the}\mathrm{remainder}\mathrm{when}2014!\mathrm{is}\mathrm{divisible}\mathrm{by}2017$$ Answered by Rasheed.Sindhi last updated on 21/Jun/19 $${Wilson}^{\prime }sTheorm:$$$$(p-1)!\equiv -1\left(modp\right):p\in \mathbb{P}$$$$\:\:\:\because\:\:\:\:\mathrm{2017}\in\mathbb{P} \…