Question Number 63858 by gunawan last updated on 10/Jul/19 $$\mathrm{if}\:\mathrm{a}_{\mathrm{1}} ,\:\mathrm{a}_{\mathrm{2}} ,\:\mathrm{a}_{\mathrm{3}} ,\:\mathrm{a}_{\mathrm{4}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{coefficient} \\ $$$$\mathrm{of}\:\mathrm{any}\:\mathrm{four}\:\mathrm{four}\:\mathrm{consecutive} \\ $$$$\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} \\ $$$$\mathrm{then}\:\frac{\mathrm{a}_{\mathrm{1}} }{\mathrm{a}_{\mathrm{2}} +\mathrm{a}_{\mathrm{1}} }+\frac{\mathrm{a}_{\mathrm{3}} }{\mathrm{a}_{\mathrm{3}} +\mathrm{a}_{\mathrm{4}}…
Question Number 129364 by shaker last updated on 15/Jan/21 Answered by mindispower last updated on 15/Jan/21 $${let}\:\alpha={e}^{{i}\frac{\pi}{\mathrm{4}}} \\ $$$$\alpha,\alpha^{\mathrm{3}} ,\alpha^{\mathrm{5}} ,\alpha^{\mathrm{7}} \:{are}\:{roots}\:{of}\:{x}^{\mathrm{4}} +\mathrm{1}=\mathrm{0} \\ $$$$\frac{{x}^{\mathrm{2}}…
Question Number 129343 by Study last updated on 15/Jan/21 $${f}\left({x}+\mathrm{1}\right)={f}\left({x}−\mathrm{1}\right)={x}^{\mathrm{2}} \:\:\:\:\:\:\:\:{f}^{−\mathrm{1}} \left({x}\right)=?? \\ $$ Commented by bramlexs22 last updated on 15/Jan/21 $$\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{x}^{\mathrm{2}} \:? \\ $$…
Question Number 63803 by aliesam last updated on 09/Jul/19 Commented by Prithwish sen last updated on 09/Jul/19 $$\left(\mathrm{x}+\mathrm{iy}\right)^{\mathrm{3}} \:=\:\frac{\left(\mathrm{1}+\sqrt{\mathrm{7}}\mathrm{i}\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{\mathrm{7}}\mathrm{i}}\:=\:\frac{\left(\mathrm{1}+\sqrt{\mathrm{7}}\mathrm{i}\right)^{\mathrm{3}} }{\mathrm{8}} \\ $$$$\:\therefore\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{y}\:=\:\frac{\sqrt{\mathrm{7}}}{\mathrm{2}} \\ $$…
Question Number 63784 by MJS last updated on 09/Jul/19 $$\mathrm{question}\:\mathrm{63639}\:\mathrm{again} \\ $$$$\mathrm{prove}: \\ $$$$\forall{z}\in\mathbb{C}:\:\mid{z}+\mathrm{1}\mid+\mid{z}^{\mathrm{2}} +{z}+\mathrm{1}\mid+\mid{z}^{\mathrm{3}} +\mathrm{1}\mid\geqslant\mathrm{1} \\ $$ Commented by Prithwish sen last updated on…
Question Number 129320 by ajfour last updated on 14/Jan/21 Commented by gaferrafie last updated on 14/Jan/21 سلام چطور میشه تو خروجی آدرس سایت را حذف کرد Answered by ajfour last updated on 14/Jan/21 $${y}=\left({x}−{p}\right)\left({x}^{\mathrm{3}}…
Question Number 129310 by I want to learn more last updated on 14/Jan/21 Commented by Tawa11 last updated on 23/Jul/21 $$\mathrm{like} \\ $$ Terms of…
Question Number 129300 by Adel last updated on 14/Jan/21 $$ \\ $$Find the polynomial divided by (x-2) the remaining 5 divided by (x-3) the remaining…
Question Number 129279 by Study last updated on 14/Jan/21 $${f}\left({x}\right)=\frac{\mathrm{7}{x}−\mathrm{3}}{\left(\mathrm{2}{x}−\mathrm{11}\right)^{{ln}\frac{\mathrm{1}}{\mathrm{7}}} }\:\:\:\:\:{in}\:{which}\:{value} \\ $$$${of}\:{x}\:{is}\:{continuty}\:?? \\ $$ Commented by Study last updated on 14/Jan/21 $${help}\:{me}! \\ $$…
Question Number 129255 by Adel last updated on 14/Jan/21 $$\mathrm{x}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} =? \\ $$ Commented by bemath last updated on 14/Jan/21 $$\mathrm{maclaurien}\:\mathrm{series} \\ $$ Terms of…