Question Number 220459 by mr W last updated on 12/May/25 $${find}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} +{a}^{\mathrm{2}} }=?\:\:\:\:\:\:\:\:\:\:\left({a}\in{R}\right) \\ $$ Answered by MrGaster last updated on 13/May/25 Commented…
Question Number 220395 by hardmath last updated on 12/May/25 $$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{x}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\underset{\boldsymbol{\mathrm{y}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:\mathrm{y}^{\mathrm{3}} \:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left(\mathrm{y}\:+\:\mathrm{2}\right)}\:=\:? \\ $$ Answered by MathematicalUser2357 last updated on…
Question Number 220391 by Lekhraj last updated on 12/May/25 Answered by MathematicalUser2357 last updated on 13/May/25 $${yes} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 220247 by Rojarani last updated on 10/May/25 Answered by Rasheed.Sindhi last updated on 11/May/25 $${x}=\frac{\mathrm{42}+\sqrt{\mathrm{63}}\:+\mathrm{3}\sqrt{\mathrm{91}}}{\mathrm{7}+\mathrm{7}\sqrt{\mathrm{7}}\:+\mathrm{7}\sqrt{\mathrm{13}}\:+\sqrt{\mathrm{91}}\:}\wedge\:{x}^{\mathrm{6}} +\mathrm{40}{x}−{k}=\mathrm{0}\:;\:{k}=? \\ $$$$\: \\ $$$${x}=\frac{\mathrm{42}+\mathrm{3}\sqrt{\mathrm{7}}\:+\mathrm{3}\sqrt{\mathrm{91}}\:}{\mathrm{7}\left(\mathrm{1}+\sqrt{\mathrm{7}}\:\right)+\sqrt{\mathrm{91}}\:\left(\sqrt{\mathrm{7}}\:+\mathrm{1}\right)} \\ $$$${x}=\frac{\cancel{\sqrt{\mathrm{7}}\:}\left(\mathrm{6}\sqrt{\mathrm{7}}+\mathrm{3}\:+\mathrm{3}\sqrt{\mathrm{13}}\:\right.}{\:\cancel{\sqrt{\mathrm{7}}\:\:}\left(\mathrm{1}+\sqrt{\mathrm{7}}\:\right)\left(\sqrt{\mathrm{7}}\:+\sqrt{\mathrm{13}}\:\right)}×\frac{\:\:\left(\mathrm{1}−\sqrt{\mathrm{7}}\:\right)\left(\sqrt{\mathrm{7}}\:−\sqrt{\mathrm{13}}\:\right)}{\:\:\:\left(\mathrm{1}−\sqrt{\mathrm{7}}\:\right)\left(\sqrt{\mathrm{7}}\:−\sqrt{\mathrm{13}}\:\right)} \\…
Question Number 220266 by Tawa11 last updated on 10/May/25 $$\mathrm{2}^{\mathrm{a}} \:\:+\:\:\mathrm{2}^{\mathrm{b}} \:\:+\:\:\mathrm{2}^{\mathrm{c}} \:\:=\:\:\mathrm{148} \\ $$ Answered by Ghisom last updated on 10/May/25 $$\mathrm{148}=\mathrm{10010100}_{\mathrm{2}} =\mathrm{128}+\mathrm{16}+\mathrm{4} \\…
Question Number 220221 by fantastic last updated on 08/May/25 $${Q}.{The}\:{density}\:{of}\:{an}\:{object}\:{of}\:{mass}\:{M}\:{is}\:\delta\:{and}\:{the}\:{density}\:{of}\:{the}\:{air}\:{is}\:\rho. \\ $$$${the}\:{mass}\:{of}\:{of}\:{the}\:{object}\:{is}\:{measured}\:{with}\:\:{the}\:{help}\:{of}\:{a}\:{metal}\:{weight}\:{of}\:{mass}\:{m}\:. \\ $$$${the}\:{density}\:{of}\:{the}\:{metal}\:{weight}\:{is}\:{d}. \\ $$$${if}\:\rho\ll\delta\:{them}\:{show}\:{that}\:{the}\:{real}\:{mass}\:{M}\:{will}\:{be} \\ $$$${m}\left(\mathrm{1}−\frac{\rho}{{d}}\:\right)\left(\mathrm{1}+\frac{\rho}{\delta}\right) \\ $$$${I}\:{have}\:{managed}\:{to}\:{M}=\frac{{m}\left(\mathrm{1}−\frac{\rho}{{d}}\right)}{\left(\mathrm{1}−\frac{\rho}{\delta}\right)} \\ $$$${but}\:{I}\:{can}\:{not}\:{figure}\:{it}\:{to}\:{the}\:{end} \\ $$$${please}\:{help} \\…
Question Number 220193 by behi834171 last updated on 07/May/25 $$\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{8}} =\mathrm{21}\boldsymbol{{x}}+\mathrm{13}\:\:\:\:\:\:\:\:\:\:;\:\:\:\:\boldsymbol{{x}}\in{R} \\ $$$$\:\:\:\:\boldsymbol{{x}}=? \\ $$ Answered by SdC355 last updated on 07/May/25 $$\:{f}\left({z}\right)={z}^{\mathrm{8}} −\mathrm{21}{z}−\mathrm{13} \\…
Question Number 220164 by mehdee7396 last updated on 06/May/25 $${if}\:\:\alpha^{\mathrm{2}} −\mathrm{5}\alpha+\mathrm{2}=\mathrm{0}\:\:\&\:\:\beta^{\mathrm{2}} −\mathrm{5}\beta+\mathrm{2}=\mathrm{0} \\ $$$${then}\:\:\frac{\mathrm{4}\alpha+\beta^{\mathrm{5}} }{\mathrm{5}\beta^{\mathrm{2}} }=? \\ $$ Answered by Rasheed.Sindhi last updated on 07/May/25…
Question Number 220094 by Nicholas666 last updated on 05/May/25 $$ \\ $$$$\:\:\:\:\mathrm{let}\:{n}\:\geqslant\:\mathrm{2}\:\in\:\mathbb{Z}\:\mathrm{and}\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:…,\:{x}_{{n}} \:\mathrm{are}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{such}\:\mathrm{that}\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:{x}_{{i}} \:=\:{n}\:,\:\mathrm{prove}\:\mathrm{that}\:\:\:\: \\ $$$$\:\:\:\:\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{x}_{{i}} ^{{n}}…
Question Number 220100 by hardmath last updated on 05/May/25 Answered by MrGaster last updated on 06/May/25 Commented by hardmath last updated on 07/May/25 $$ \\…