Category: Algebra

Question Number 142740 by mathdanisur last updated on 04/Jun/21 $$\frac{a}{b+c}=\frac{b}{a+c}=\frac{c}{a+b};a\cdot b\cdot c=12$$$$(b+c)\cdot (a+c)\cdot (a+b)=?$$ Commented by MJS_new last updated on 05/Jun/21 $$\mathrm{I}\mathrm{found}2\mathrm{possibilities}$$$$\left(\mathrm{1}\right)\:{a}={b}={c}=\sqrt[{\mathrm{3}}]{\mathrm{12}}\:\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{96} \…

Question Number 11661 by @ANTARES_VY last updated on 29/Mar/17 $$8{\mathbf{x}}^3-6\mathbf{x}+1=0.$$$$\mathbf{Solves}\dots \mathbf{equation}$$$${\mathbf{x}}_1=?{\mathbf{x}}_2=?$$ Answered by Joel576 last updated on…

Question Number 11648 by uni last updated on 29/Mar/17 $$\mid \mathrm{x}\mid <\mathrm{l}$$$$\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}{\mathrm{x}}^{\mathrm{n}}=?$$ Answered by Nayon last updated on 29/Mar/17 $$…

Question Number 142710 by loveineq last updated on 04/Jun/21 $$\mathrm{Let}k\mathrm{be}\mathrm{non}-\mathrm{negative}\mathrm{real}\mathrm{numbers}\mathrm{and}n\in {\mathrm{N}}^{+}⩾1.$$$$\mathrm{Prove}\mathrm{that}$$$$\left(\frac{4-k}{4+k}\right)\left(\frac{12-k}{12+k}\right)\dots \left[\frac{2n(n+1)-k}{2n(n+1)+k}\right]⩽\frac{n+k+1}{(n+1)(k+1)}$$$$$$ Answered by loveineq last updated on…

Question Number 77154 by Boyka last updated on 03/Jan/20 Commented by Boyka last updated on 04/Jan/20 $$\mathrm{sir}\mathrm{w},\mathrm{mind}\mathrm{is}\mathrm{power}$$ Commented by mr W last updated…