Category: Algebra

Question Number 118023 by 1549442205PVT last updated on 14/Oct/20 $$$$$$..calculus..$$$$x,y,z\in {\mathbb{R}}^{+}and{x}^2+y^2+z^2=1$$$$$$$$find$$$$\:\:\:\:{min}_{{x},{y},{z}\in\mathbb{R}^{+\:\:\:\:} }…

Question Number 118002 by mmmmmm1 last updated on 14/Oct/20 Answered by TANMAY PANACEA last updated on 14/Oct/20 $$x^3+\frac{1}{x^3}+x+\frac{1}{x}$$$${(x+\frac{1}{x})}^3-3(x+\frac{1}{x})+(x+\frac{1}{x})$$$${now}\:{x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\:+\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}\:=\mathrm{6}…

Question Number 52449 by maxmathsup by imad last updated on 07/Jan/19 $$letj=e^{\frac{i2\pi }{3}}andP\left(x\right)={(1+jx)}^n-{(1-jx)}^{n}withnintegrnatural$$$$1)findrootsofP\left(x\right)$$$$2)factorizeP\left(x\right)insideC\left[x\right]$$$$3)calculate{\int }_0^{1}P\left(x\right)dx.$$$$\left.\mathrm{4}\right)\:{decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{P}\left({x}\right)}…

Question Number 117972 by Ar Brandon last updated on 14/Oct/20 $$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{surjections}\mathrm{of}\{1,2,3,4\}\mathrm{onto}\{\mathrm{x},\mathrm{y}\}\mathrm{is}$$$$\left(\mathrm{A}\right)16\left(\mathrm{B}\right)8\left(\mathrm{C}\right)14\left(\mathrm{D}\right)6$$ Answered by Lordose last updated on 14/Oct/20 $$\mathrm{N}=\:\mathrm{2}^{\mathrm{n}\left(\mathrm{A}\right)−\mathrm{1}} =\:\mathrm{2}^{\mathrm{3}} =\mathrm{8}…

Question Number 52412 by Tawa1 last updated on 07/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 08/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 08/Jan/19 Commented by…