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}}…
Question Number 157628 by mr W last updated on 25/Oct/21 $${find} \\ $$$$\left({C}_{\mathrm{0}} ^{\mathrm{100}} \right)^{\mathrm{2}} +\left({C}_{\mathrm{2}} ^{\mathrm{100}} \right)^{\mathrm{2}} +\left({C}_{\mathrm{4}} ^{\mathrm{100}} \right)^{\mathrm{2}} +\left({C}_{\mathrm{6}} ^{\mathrm{100}} \right)^{\mathrm{2}} +…+\left({C}_{\mathrm{100}}…
Question Number 92084 by Power last updated on 04/May/20 Answered by MJS last updated on 04/May/20 $$\mathrm{obviously}\:{x}_{\mathrm{0}} ={y}_{\mathrm{0}} =\mathrm{0} \\ $$$$\mathrm{let}\:{x}\neq\mathrm{0}\:\wedge\:{y}={px}\:\wedge\:{p}\neq\mathrm{0} \\ $$$$\begin{cases}{{x}\left(\left({p}^{\mathrm{5}} +\mathrm{1}\right){x}^{\mathrm{4}} −\mathrm{33}{p}\right)=\mathrm{0}}\\{{x}\left(\mathrm{3}{p}^{\mathrm{2}}…
Question Number 157604 by mnjuly1970 last updated on 25/Oct/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Q}{uestion}\: \\ $$$$\:{find}\:{the}''\:{minimum}''\:{value}\:{of}: \\ $$$$ \\ $$$${f}\:\left({x}\right):=\:\mid\mathrm{1}+{x}\mid+\mid\:\mathrm{2}+{x}\mid\:+\:\mid\mathrm{4}\:+\mathrm{2}{x}\mid \\ $$$$ \\ $$ Commented by mr…
Question Number 157593 by metamorfose last updated on 25/Oct/21 $${let}\:{f}:{C}\rightarrow{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:{z}\rightarrow{min}\left({y}−\left[{y}\right],\left[{y}+\mathrm{1}\right]−{y}\right)\:,\:{y}={Im}\left({z}\right) \\ $$$${let}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} ,\:{n}\in{N}^{\ast} \\ $$$${evaluate}\:{S}_{{n}} =\underset{\mathrm{0}\leqslant{k}<{n}} {\sum}{f}\left({w}^{{k}} \right) \\ $$ Terms of Service…
Question Number 157592 by metamorfose last updated on 25/Oct/21 $${let}\:{A}=\left\{\overset{.} {\mathrm{0}},\overset{.} {\mathrm{1}},\overset{.} {\mathrm{2}}\right\} \\ $$$${prove}\:{that}\:{every}\:{application}\:{from}\:{A}\: \\ $$$${to}\:{A}\:{is}\:{a}\:\mathrm{2}{nd}\:{degree}\:{polynom} \\ $$ Terms of Service Privacy Policy Contact:…