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known-x-y-3-ask-min-x-2-1-y2-4-

Question Number 211529 by MrGaster last updated on 12/Sep/24 $$\mathrm{known}:\boldsymbol{{x}}+\boldsymbol{\mathrm{y}}=\mathrm{3},\mathrm{ask}: \\ $$$$\boldsymbol{\mathrm{min}}\left(\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}+\sqrt{\boldsymbol{\mathrm{y}}\mathrm{2}−\mathrm{4}}\right)=? \\ $$ Answered by MrGaster last updated on 12/Sep/24 $$\mathrm{1}.\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}+\sqrt{\left(\mathrm{3}+\boldsymbol{{x}}\right)^{\mathrm{2}} −\mathrm{4}}…

for-example-I-say-Bob-is-born-in-1900s-there-the-symbol-of-s-means-century-what-kind-of-word-it-taken-from-

Question Number 211515 by Davidtim last updated on 11/Sep/24 $${for}\:{example}\:{I}\:{say}\:{Bob}\:{is}\:{born}\:{in} \\ $$$$\mathrm{1900}{s},\:{there}\:{the}\:{symbol}\:{of}\:\left({s}\right)\:{means} \\ $$$${century}.\:{what}\:{kind}\:{of}\:{word}\:{it}\:{taken} \\ $$$${from}? \\ $$ Commented by Frix last updated on 11/Sep/24…

0-9999-a-b-

Question Number 211434 by Davidtim last updated on 09/Sep/24 $$\mathrm{0}.\mathrm{9999}….=?\frac{{a}}{{b}} \\ $$ Answered by Rasheed.Sindhi last updated on 09/Sep/24 $${n}=\mathrm{0}.\mathrm{9999}…. \\ $$$$\mathrm{10}{n}=\mathrm{9}.\mathrm{9999} \\ $$$$\mathrm{10}{n}−{n}=\mathrm{9} \\…

Question-211419

Question Number 211419 by maryaaaa last updated on 08/Sep/24 Answered by mahdipoor last updated on 08/Sep/24 $$\left.{salam}\:\::\right) \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{2}\left[{x}\right]\:\:\:,\:\:\:{f}\left(−\frac{{f}\left(\sqrt{\mathrm{3}}\right)}{\mathrm{2}}\right)=? \\ $$$${f}\left(\sqrt{\mathrm{3}}\right)=\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} −\mathrm{2}\left[\sqrt{\mathrm{3}}\right]=\mathrm{3}−\mathrm{2}×\mathrm{1}=\mathrm{1} \\ $$$${f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=\left(−\mathrm{0}.\mathrm{5}\right)^{\mathrm{2}}…

Question-211415

Question Number 211415 by AlagaIbile last updated on 08/Sep/24 Commented by loredcs2357 last updated on 11/Oct/24 $$\mathrm{Let}\:{S}\left({n}\right)=\underset{{k}\leqslant{n}} {\sum}\mathrm{lcm}\left({k},{n}\right). \\ $$$$\mathrm{It}'\mathrm{s}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{see}\:\mathrm{that}\:{S}\left({n}\right)=\frac{{n}}{\mathrm{2}}\left[\underset{{d}\mid{n}} {\sum}\varphi\left({d}^{\mathrm{2}} \right)+\mathrm{1}\right].\:\mathrm{Moreover}\:\mathrm{we}\:\mathrm{have}: \\ $$$${f}\left({n}\right)=\underset{{d}\mid{n}} {\sum}\varphi\left({d}^{\mathrm{2}}…