Question Number 3775 by Yozzii last updated on 20/Dec/15 $${Let}\:{a}_{{i}} \:\left(\mathrm{1}\leqslant{i}\leqslant\mathrm{10}\right)\:{be}\:{the}\:{roots}\:{of}\:{the} \\ $$$${equation}\:\underset{{m}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}{mx}^{{m}} =\mathrm{0}.\:{Prove}\:{that} \\ $$$$\mathrm{100}\underset{{i}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}\left({a}_{{i}} ^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{61}. \\ $$$$\left({An}\:{algebra}\:{question}\:{as}\:{seen}\:{on}\:{Brilliant}.\right) \\…
Question Number 3768 by Filup last updated on 19/Dec/15 $$\mathrm{let}\:\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{be}\:\mathrm{irrational}. \\ $$$${That}\:{is}: \\ $$$${a},\:{b},\:{c}\in\mathbb{R}/\mathbb{Q} \\ $$$$ \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{for}: \\ $$$${c}=\frac{{a}}{{b}}? \\ $$ Commented by 123456…
Question Number 69297 by ajfour last updated on 22/Sep/19 Commented by ajfour last updated on 22/Sep/19 $${If}\:{the}\:{graph}\:{is}\:{a}\:{cubic} \\ $$$$\:\:\:\:{y}={x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${find}\:{point}\:{of}\:{intersection}\:{of} \\ $$$${the}\:{red}\:{and}\:{blue}\:{lines}.…
Question Number 69296 by ozodbek last updated on 22/Sep/19 Commented by Prithwish sen last updated on 22/Sep/19 $$\mathrm{can}\:\mathrm{you}\:\mathrm{post}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{please}? \\ $$ Commented by MJS last updated…
Question Number 69293 by A8;15: last updated on 22/Sep/19 Commented by MJS last updated on 22/Sep/19 $$\mathrm{great},\:\mathrm{you}'\mathrm{ve}\:\mathrm{been}\:\mathrm{faster}\:\mathrm{than}\:\mathrm{me} \\ $$$$\mathrm{but}\:\mathrm{also}\:{x}=\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution} \\ $$ Commented by Rasheed.Sindhi last…
Question Number 134817 by bramlexs22 last updated on 07/Mar/21 $$ \\ $$What is the maximum value of abc if a+b+c = 5 and ab+bc+ca =…
Question Number 69276 by mr W last updated on 22/Sep/19 $${f}\left({x}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mid{x}+{k}\mid \\ $$$$\left(\mathrm{1}\right)\:{find}\:{the}\:{values}\:{of}\:{x}\:{such}\:{that}\:{f}\left({x}\right)\: \\ $$$${is}\:{minumum}. \\ $$$$\left(\mathrm{2}\right)\:{fund}\:{the}\:{roots}\:{of}\:{f}\left({x}\right)−{m}=\mathrm{0} \\ $$$$ \\ $$$${as}\:{example}\:{you}\:{can}\:{set}\:{n}=\mathrm{100},\:{m}=\mathrm{2500}. \\ $$…
Question Number 3734 by prakash jain last updated on 19/Dec/15 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{{n}}{\mathrm{2}^{{n}} }=? \\ $$ Answered by prakash jain last updated on 19/Dec/15 $${a}_{{n}}…
Question Number 3735 by prakash jain last updated on 19/Dec/15 $$\mathrm{Prove} \\ $$$$\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{{mn}}{\mathrm{2}^{{m}+{n}} }=\mathrm{4} \\ $$ Commented by prakash jain last…
Question Number 3716 by Yozzii last updated on 19/Dec/15 $$\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{m}+{n}+{mn}}{\mathrm{2}^{{m}} \left(\mathrm{2}^{{m}} +\mathrm{2}^{{n}} \right)}=?\: \\ $$$$\left({Not}\:{originally}\:{produced}\:{by}\:{me}.\right) \\ $$ Commented by prakash jain…