Category: Algebra

Question Number 143234 by mathdanisur last updated on 11/Jun/21 Answered by mr W last updated on 11/Jun/21 $$F=x^3+y^3+z^3+\lambda (\alpha x+\alpha y+\gamma z-1)$$$$\frac{\partial{F}}{\partial{x}}=\mathrm{3}{x}^{\mathrm{2}} +\lambda\alpha=\mathrm{0}\: \…

Question Number 143229 by loveineq last updated on 11/Jun/21 $$\mathrm{Let}a,b,c⩾0\mathrm{and}(1+a)(1+b)(1+c)=8.$$$$\mathrm{Prove}\mathrm{that}$$$$(a+\frac{2b+1}{a+b+1})(b+\frac{2c+1}{b+c+1})(c+\frac{2a+1}{c+a+1})⩾8$$$$$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 12126 by tawa last updated on 13/Apr/17 Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 $$a^2+b^2+c^2+2ab+2ac+2bc=0$$$$\Rightarrow ab+bc+ca=-21$$$${A}=\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right) \…

Question Number 12109 by FilupS last updated on 13/Apr/17 $$\mathrm{show}\mathrm{that}:$$$$\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{n+1}}{n}=\ln \left(2\right)$$$$\mathrm{please}\mathrm{show}\mathrm{your}\mathrm{working}$$ Terms of Service Privacy Policy Contact:…

Question Number 12096 by sin (x) last updated on 13/Apr/17 Answered by ajfour last updated on 13/Apr/17 Commented by ajfour last updated on 13/Apr/17 $${As}\:\:\:{CD}={AE}…