Category: Algebra

Question Number 21877 by FilupS last updated on 06/Oct/17 $$x{=}^3\sqrt{7+5\sqrt{2}}{+}^3\sqrt{7-5\sqrt{2}}$$$$$$$$1.\mathrm{According}\mathrm{to}\mathrm{a}\mathrm{video},x=2$$$$$$$$2.\mathrm{According}\mathrm{to}\mathrm{WolframAlpha},$$$$x\approx 0.2071+0.3587i\mathrm{for}“\mathrm{principal}{\mathrm{root}}^{″}$$$$\mathrm{and}\:\:\:{x}=\mathrm{2}\sqrt{\mathrm{2}}\:\:\mathrm{for}\:“\mathrm{real}-\mathrm{valued}\:\mathrm{root}'' \…

Question Number 152946 by john_santu last updated on 03/Sep/21 $$\frac{4038}{1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\dots +\frac{1}{1+2+3+4+\dots +2019}}=?$$ Commented by mathdanisur last updated on 03/Sep/21 $$▴\frac{2\cdot 2019}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots +\frac{1}{1+2+3+\dots +2019}}$$$$\mathbf{A}=1+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots +\frac{1}{1+2+\dots +2019}$$$$\boldsymbol{\mathrm{A}}\:=\:\mathrm{1}\:+\:\frac{\mathrm{2}}{\mathrm{2}\centerdot\mathrm{3}}\:+\:\frac{\mathrm{2}}{\mathrm{3}\centerdot\mathrm{4}}\:+\:…\:+\:\frac{\mathrm{2}}{\mathrm{2019}\centerdot\mathrm{2020}} \…

Question Number 21867 by Tinkutara last updated on 05/Oct/17 $$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{points}\mathrm{in}\mathrm{the}\mathrm{cartesian}$$$$\mathrm{plane}\mathrm{with}\mathrm{integral}\mathrm{coordinates}$$$$\mathrm{satisfying}\mathrm{the}\mathrm{inequalities}\mid x\mid ⩽4,\mid y\mid ⩽$$$$4\mathrm{and}\mid x-y\mid ⩽4\mathrm{is}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 87382 by mathocean1 last updated on 04/Apr/20 $$\mathrm{Show}\mathrm{that}\tan \frac{5\pi }{12}\mathrm{is}\mathrm{a}\mathrm{solution}\mathrm{of}\mathrm{this}$$$$\mathrm{equation}:x^3-3x^2-3x+1=0$$ Answered by ajfour last updated on 04/Apr/20 $${x}^{\mathrm{3}} +\mathrm{1}=\mathrm{3}{x}\left({x}+\mathrm{1}\right)…

Question Number 152912 by mathdanisur last updated on 03/Sep/21 Answered by ghimisi last updated on 03/Sep/21 $$\mathrm{\Sigma }\frac{a}{2b+3c}=\mathrm{\Sigma }\frac{a^2}{2ab+3ac}⩾\frac{{(a+b+c)}^2}{5(ab+bc+ac)}⩾\frac{3(ab+bc+ca)}{5(ab+bc+ac)}=\frac{3}{5}$$ Commented by ghimisi last…