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…
Question Number 157663 by mathlove last updated on 26/Oct/21 Answered by TheSupreme last updated on 26/Oct/21 $$\mathrm{6}\:\:\mathrm{5}\:\:\mathrm{4}\:\:\mathrm{3}\:\:\mathrm{2}\:\:\mathrm{1}\:\:\mathrm{0} \\ $$$$\mathrm{1}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{2}\:\:{x}^{\mathrm{5}} \\ $$$$\mathrm{1}\:+\:\mathrm{3}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{2}\:\: \\ $$$$/\:−\mathrm{3}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{2}\:−\mathrm{3}{x}^{\mathrm{4}} \\ $$$$/\:−\mathrm{3}\:\:−\mathrm{9}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}\:\:+\mathrm{0}…
Question Number 26583 by abdo imad last updated on 27/Dec/17 $${find}\:{the}\:{decomposition}\:{in}\:\mathbb{C}\left[{x}\right]\:{then}\:\mathbb{R}\left[{x}\right] \\ $$$${for}\:{the}\:{rationsl}\:{fraction} \\ $$$${F}\left({x}\right)=\:\:\frac{\mathrm{1}\:}{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:\:.{with}\:{n}\:{integer}\:{not}\:\mathrm{0} \\ $$ Commented by abdo imad last updated on…
Question Number 26582 by abdo imad last updated on 27/Dec/17 $${p}\:{is}\:{a}\:{polynomial}\:{having}\:{the}\:{roots}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,…{x}_{{n}} \\ $$$${with}\:{x}_{{i}} \neq\:{x}_{{j}} \:{fori}\neq{j}\:{give}\:{the}\:{decomposition} \\ $$$${of}\:{the}\:{fravtion}\:{F}\left({x}\right)=\:\frac{{p}^{'} \left({x}\right)}{{p}\left({x}\right)} \\ $$ Commented by abdo…
Question Number 157637 by quvonch3737 last updated on 25/Oct/21 $$\:\:\:\:\:\:\mathrm{3}^{{x}} =\mathrm{2}^{{x}} {y}+\mathrm{1} \\ $$$$\:\:\:\:\:\left\{\boldsymbol{{x}}:\boldsymbol{{y}}\right\}\:\varepsilon\mathbb{N}.\: \\ $$ Answered by MathsFan last updated on 25/Oct/21 $$\mathrm{3}^{{x}} −\mathrm{2}^{{x}}…
Question Number 92102 by M±th+et+s last updated on 04/May/20 $${how}\:{can}\:{we}\:{factorize}\:\:\:{x}^{\mathrm{5}} −\mathrm{1}\:\:? \\ $$ Commented by mathmax by abdo last updated on 05/May/20 $${complex}\:{method}\:{z}^{\mathrm{5}} =\mathrm{1}\:\:\:{with}\:{z}\:={re}^{{i}\theta} \:\Rightarrow{r}^{\mathrm{5}}…