Question Number 26642 by Sr@2004 last updated on 27/Dec/17 $$\mathrm{9}{x}^{\mathrm{2}} +\mathrm{41}{x}−\mathrm{204}=\mathrm{0}.\:{solved}\:{it}. \\ $$ Answered by Rasheed.Sindhi last updated on 27/Dec/17 $$\mathrm{x}=\frac{−\mathrm{41}\pm\sqrt{\mathrm{41}^{\mathrm{2}} −\mathrm{4}\left(\mathrm{9}\right)\left(−\mathrm{204}\right)}}{\mathrm{2}\left(\mathrm{9}\right)} \\ $$$$\mathrm{x}=\frac{−\mathrm{41}\pm\mathrm{95}}{\mathrm{18}}=\mathrm{3},−\mathrm{7}\frac{\mathrm{5}}{\mathrm{9}} \\…
Question Number 157701 by MathSh last updated on 26/Oct/21 $$\mathrm{a};\mathrm{b};\mathrm{c}\in\mathbb{N} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}\:+\:\frac{\mathrm{1}}{\mathrm{b}\:+\:\frac{\mathrm{1}}{\mathrm{c}}}}\:=\:\frac{\mathrm{16}}{\mathrm{37}}\:\:\:\Rightarrow\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=? \\ $$ Answered by mindispower last updated on 26/Oct/21 $$\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{5}}{\mathrm{16}}}=\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{5}}}} \\ $$ Commented…
Question Number 157695 by amin96 last updated on 26/Oct/21 Answered by Rasheed.Sindhi last updated on 26/Oct/21 $${x}^{\mathrm{16}} +\frac{\mathrm{1}}{{x}^{\mathrm{16}} }=\left({x}^{\mathrm{8}} +\frac{\mathrm{1}}{{x}^{\mathrm{8}} }\right)^{\mathrm{2}} −\mathrm{2}=\mathrm{2207} \\ $$$${x}^{\mathrm{8}} +\frac{\mathrm{1}}{{x}^{\mathrm{8}}…
Question Number 157694 by ajfour last updated on 26/Oct/21 $$\:\:\:{x}^{\mathrm{3}} ={x}+{c}\:\:\:\:\:;\:\:\:\:\mathrm{0}<{c}\leqslant\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$${find}\:{x},\:{without}\:{trigonometric} \\ $$$${cubic}\:{formula}. \\ $$ Answered by ajfour last updated on 26/Oct/21 Terms…
Question Number 157687 by MathSh last updated on 26/Oct/21 $$\mathrm{if}\:\:\:\mathrm{A}\:;\:\mathrm{a}\:;\:\mathrm{b}\:\in\:\mathbb{Z}^{+} \:\:\mathrm{and}\:\:\mathrm{6}\centerdot\mathrm{40}!=\mathrm{A}\centerdot\mathrm{2}^{\boldsymbol{\mathrm{a}}} \centerdot\mathrm{3}^{\boldsymbol{\mathrm{b}}} \\ $$$$\mathrm{find}\:\:\:\left(\mathrm{a}+\mathrm{b}\right)_{\boldsymbol{\mathrm{max}}} \:=\:? \\ $$ Commented by Rasheed.Sindhi last updated on 26/Oct/21 $$\left(\mathrm{a}+\mathrm{b}\right)_{\boldsymbol{\mathrm{max}}}…
Question Number 92151 by jagoll last updated on 05/May/20 $$\mathrm{If}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{value}\: \\ $$$$\mathrm{pq}\:+\:\mathrm{2p}+\mathrm{2q}\:=\:\mathrm{217}\: \\ $$$$\mathrm{find}\:\mathrm{p}+\mathrm{q}\: \\ $$ Commented by john santu last updated on…
Question Number 92146 by kpn last updated on 05/May/20 $${how}\:{do}\:{i}\:{find}\:{integers}\:{that}\:{satisfy} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{2017} \\ $$ Commented by Prithwish Sen 1 last updated on 05/May/20…
Question Number 157686 by MathSh last updated on 26/Oct/21 $$\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)-\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{25}\right)=\mathrm{72} \\ $$$$\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{2}\right)\:=\:? \\ $$ Answered by tounghoungko last updated on 26/Oct/21 $$\Rightarrow{f}\left({x}\right)={f}\left({x}+\mathrm{1}\right)−\mathrm{3} \\ $$$$\Rightarrow{f}\left(\mathrm{25}\right)={f}\left(\mathrm{24}\right)−\mathrm{3} \\…
Question Number 92137 by hore last updated on 05/May/20 $$\int\frac{\mathrm{2}{x}}{\mathrm{1}+{x}} \\ $$ Commented by john santu last updated on 05/May/20 $$\int\:\frac{\mathrm{2}{x}\:{dx}}{{x}+\mathrm{1}}\:=\:\int\:\frac{\mathrm{2}\left({x}+\mathrm{1}\right)−\mathrm{2}}{{x}+\mathrm{1}}\:{dx} \\ $$$$=\:\int\:\mathrm{2}\:−\:\frac{\mathrm{2}}{{x}+\mathrm{1}}\:{dx}\: \\ $$$$=\:\mathrm{2}{x}−\mathrm{2}\:\mathrm{ln}\mid{x}−\mathrm{1}\mid\:+\:\mathrm{c}\:…
Question Number 157664 by cortano last updated on 26/Oct/21 $$\:\begin{cases}{{ax}+{by}=\mathrm{7}}\\{{ax}^{\mathrm{2}} +{by}^{\mathrm{2}} =\mathrm{49}}\\{{ax}^{\mathrm{3}} +{by}^{\mathrm{3}} =\mathrm{133}}\\{{ax}^{\mathrm{4}} +{by}^{\mathrm{4}} =\mathrm{406}}\end{cases} \\ $$$$\:\Rightarrow\mathrm{2014}{x}+\mathrm{2014}{y}−\mathrm{100}{a}−\mathrm{100}{b}−\mathrm{2014}{xy}=? \\ $$ Commented by mr W last…