Category: Algebra

Question Number 185972 by Michaelfaraday last updated on 30/Jan/23 Answered by Rasheed.Sindhi last updated on 30/Jan/23 $$x=\sqrt[3]{p}+\frac{1}{\sqrt[3]{p}},y=\sqrt{p}+\frac{1}{\sqrt{p}}$$$$Showthat{y}^2-2=x(x^2-3)$$$${x}^{\mathrm{3}} =\left(\sqrt[{\mathrm{3}}]{{p}}\:+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{p}}\:}\right)^{\mathrm{3}} ={p}+\frac{\mathrm{1}}{{p}}+\mathrm{3}\left(\sqrt[{\mathrm{3}}]{{p}}\:+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{p}}\:}\right)…

Question Number 54857 by Tawa1 last updated on 13/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 13/Feb/19 $$\frac{d^{2}y}{{dx}^2}+\lambda y=0$$$$y=e^{mx}$$$${m}^{\mathrm{2}} {e}^{{mx}} +\lambda{e}^{{mx}}…

Question Number 120355 by TITA last updated on 30/Oct/20 Commented by TITA last updated on 30/Oct/20 $$pleasehelp$$ Commented by TITA last updated on…

Question Number 185876 by MATHEMATICSAM last updated on 29/Jan/23 $$x=\frac{2ab}{a+b}\mathrm{then}\mathrm{prove}\mathrm{that}$$$$\frac{x+a}{x-a}+\frac{x+b}{x-b}=2$$ Answered by Rasheed.Sindhi last updated on 29/Jan/23 $$x=\frac{2ab}{a+b}\mathrm{then}\mathrm{prove}\mathrm{that}$$$$\frac{{x}\:+\:{a}}{{x}\:−\:{a}}\:+\:\frac{{x}\:+\:{b}}{{x}\:−\:{b}}\:=\:\mathrm{2} \…

Question Number 120324 by mathocean1 last updated on 30/Oct/20 $$\mathrm{we}\mathrm{are}\mathrm{in}\mathbb{C}.$$$$\left(\mathrm{E}\right):{\mathrm{z}}^3+(4-5\mathrm{i}){\mathrm{z}}^2+(8-20\mathrm{i})\mathrm{z}-40\mathrm{i}=0$$$$1)\mathrm{Show}\mathrm{that}\left(\mathrm{E}\right)\mathrm{has}\mathrm{one}\mathrm{imaginary}\mathrm{pure}\mathrm{root}$$$$2)\mathrm{solve}\left(\mathrm{E}\right)$$ Answered by Olaf last updated…