Question Number 147572 by liberty last updated on 22/Jul/21 $$\:\:\:\underset{{n}\geqslant\mathrm{1}} {\sum}\:\frac{\mathrm{4}{n}−\mathrm{3}}{\left({n}^{\mathrm{2}} +\mathrm{2}{n}\right)\left({n}+\mathrm{3}\right)}\:=? \\ $$ Answered by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{let}\:\mathrm{S}=\sum_{\mathrm{n}=\mathrm{1}} ^{\infty}…
Question Number 147566 by mathdanisur last updated on 21/Jul/21 $${x}^{\mathrm{3}} \:+\:\mathrm{3367}\:=\:\mathrm{2}^{\boldsymbol{{n}}} \:\:\Rightarrow\:{x}\:;\:{n}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 21/Jul/21 $${x}^{\mathrm{3}} +\mathrm{3367}\:=\:\mathrm{2}^{{n}} \\ $$$$\mathrm{Solution}\:\mathrm{for}\:{x}\in\mathbb{N}.…
Question Number 82031 by M±th+et£s last updated on 17/Feb/20 $${find}\:{x},{y} \\ $$$$\begin{cases}{\mathrm{5}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{4}{x}−\mathrm{3}{y}}\\{\mathrm{4}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{3}{x}−\mathrm{2}{y}}\end{cases} \\ $$ Answered by MJS last updated on 17/Feb/20…
Question Number 147557 by mathdanisur last updated on 21/Jul/21 $${Simlify} \\ $$$$\left(\frac{\mathrm{1}+\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}}}\:−\:\frac{\sqrt{\mathrm{1}+{x}}}{\mathrm{1}+\sqrt{{x}}}\right)^{\mathrm{2}} -\:\left(\frac{\mathrm{1}−\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}}}\:−\:\frac{\sqrt{\mathrm{1}+{x}}}{\mathrm{1}−\sqrt{{x}}}\right)^{\mathrm{2}} \\ $$ Answered by Rasheed.Sindhi last updated on 21/Jul/21 $$\left(\underset{{a}} {\underbrace{\frac{\mathrm{1}+\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}}}\:}}−\:\frac{\sqrt{\mathrm{1}+{x}}}{\mathrm{1}+\sqrt{{x}}}\right)^{\mathrm{2}} -\:\left(\underset{{b}}…
Question Number 147553 by Ar Brandon last updated on 21/Jul/21 Answered by ArielVyny last updated on 22/Jul/21 $$\left.\mathrm{1}\right){Formule}\:{de}\:{Poincarre}\:{se}\:{demontre}\:{par}\: \\ $$$${reccurence} \\ $$$$\left.\mathrm{2}\right){soit}\:{f}\:\:{l}'{application}\:{qui}\:{a}\:{une}\:{lettre}\:{i}\:{on}\: \\ $$$${associe}\:{un}\:{destinataire}\:{ou}\:{f}\left({i}\right)\:{est}\:{la}\:{lettre} \\…
Question Number 147529 by mathdanisur last updated on 21/Jul/21 $${if}\:\:\:{a}_{\boldsymbol{{n}}+\mathrm{1}} \:=\:\sqrt{{a}_{\mathrm{1}} \:+\:{a}_{\boldsymbol{{n}}} } \\ $$$${find}\:\:\underset{\boldsymbol{{x}}\rightarrow\infty} {{lim}a}_{\boldsymbol{{n}}} \:=\:? \\ $$ Commented by mathdanisur last updated on…
Question Number 147500 by mathdanisur last updated on 21/Jul/21 $${x}^{\mathrm{2}} \:-\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:=\:\mathrm{22} \\ $$$${what}\:{is}\:{the}\:{number}\:{of}\:{complete} \\ $$$${solutions}\:{that}\:{satisf}\:{the}\:{equation} \\ $$$$\left({x};{y}\right).? \\ $$ Commented by Mrsof last updated…
Question Number 147488 by mathdanisur last updated on 21/Jul/21 $${if}\:\:{x};{y};{z}\geqslant\mathrm{1}\:\:{then}: \\ $$$$\frac{\mathrm{1}}{\mathrm{3}{xy}−\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{3}{yz}−\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{3}{zx}−\mathrm{1}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}{xyz}} \\ $$ Answered by mindispower last updated on 21/Jul/21 $${in}\:{firt} \\ $$$$\mathrm{1}\leqslant{xy},{xy}=\frac{{xyz}}{{z}} \\…
Question Number 81944 by M±th+et£s last updated on 16/Feb/20 $${show}\:{that}\: \\ $$$${cot}\left(\mathrm{40}°\right)−{cot}\left(\mathrm{50}°\right)=\mathrm{2}{tan}\left(\mathrm{10}°\right) \\ $$$${cos}\left(\mathrm{70}°\right)\:{cos}\left(\mathrm{50}^{°} \right)\:{cos}\left(\mathrm{10}^{°} \right)=\frac{\sqrt{\mathrm{3}}}{\mathrm{8}} \\ $$ Answered by TANMAY PANACEA last updated on…
Question Number 81942 by TawaTawa last updated on 16/Feb/20 Answered by TANMAY PANACEA last updated on 16/Feb/20 $${for}\:{bank}\:{p}\:{interest}=\frac{\mathrm{3000}×\mathrm{1}×{x}}{\mathrm{100}}=\mathrm{30}{x} \\ $$$${for}\:{bank}\:{Q}\:{interst}=\frac{\mathrm{2000}×\mathrm{1}×{y}}{\mathrm{100}}=\mathrm{20}{y} \\ $$$${as}\:{per}\:{second}\:{condition} \\ $$$${interest}\:{in}\:{bank}\:{p}=\frac{\mathrm{2000}×\mathrm{1}×{x}}{\mathrm{100}}=\mathrm{20}{x} \\…