Question Number 180953 by depressiveshrek last updated on 19/Nov/22 $${What}'{s}\:{the}\:{smallest}\:{value}\:{of} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\frac{\mathrm{1}}{{ab}}\:{for}\:{a},\:{b}>\mathrm{0}? \\ $$ Answered by mr W last updated on 19/Nov/22 $${a}^{\mathrm{2}}…
Question Number 180943 by Shrinava last updated on 19/Nov/22 $$\mathrm{if}:\:\:\:\overline {\mathrm{a}\:,\:\mathrm{bc}}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{50}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=? \\ $$ Answered by mahdipoor last updated on 19/Nov/22 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{50}}=\mathrm{1}.\mathrm{56} \\ $$$$\mathrm{1}+\mathrm{5}+\mathrm{6}=\mathrm{12}…
Question Number 180938 by Shrinava last updated on 19/Nov/22 $$\overline {\mathrm{ab}}\:+\:\overline {\mathrm{ba}}\:=\:\overline {\mathrm{c3}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{2c}=? \\ $$ Answered by Rasheed.Sindhi last updated on 19/Nov/22 $$\overline…
Question Number 49857 by afachri last updated on 11/Dec/18 $$\mathrm{Please}\:\mathrm{guide}\:\mathrm{me}\:\mathrm{Sir}.\:\mathrm{I}\:\mathrm{was}\:\mathrm{trying}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\mathrm{this}\:\mathrm{eq}\:\mathrm{for}\:\mathrm{searching}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:{x}. \\ $$$$\mathrm{eq}\:\mathrm{is}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid{x}\:−\:\mathrm{2}\mid\:<\:\mathrm{3}\mid{x}\:+\:\mathrm{7}\mid \\ $$$$\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}\:\mathrm{whom}\:\mathrm{i}\:\mathrm{got}\::\:\:\:−\frac{\mathrm{23}}{\mathrm{2}}\:<\:{x}\:<\:−\frac{\mathrm{19}}{\mathrm{4}} \\ $$$$\mathrm{but}\:\mathrm{the}\:\mathrm{result}\:\mathrm{do}\:\mathrm{not}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{eq},\:\mathrm{instead} \\ $$$$\mathrm{i}\:\mathrm{put}\:{x}\:>\:−\mathrm{4}\:,\:\mathrm{they}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{eq}.\: \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{out}\:\mathrm{of}\:\mathrm{this}\:\mathrm{pickle}. \\…
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Question Number 180923 by Shrinava last updated on 19/Nov/22 Answered by aleks041103 last updated on 20/Nov/22 $${Forbenius}:\:{A},{B},{C}\in{M}_{{n}} \left(\mathbb{F}\right) \\ $$$${rk}\left({abc}\right)+{rk}\left({b}\right)\geqslant{rk}\left({ab}\right)+{rk}\left({bc}\right) \\ $$$${b}={A} \\ $$$${a}={A}^{\mathrm{3}} \\…
Question Number 180896 by mr W last updated on 18/Nov/22 $${find}\:{the}\:{maximum}\:{of}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mathrm{sin}^{\mathrm{3}} \:{x}_{{i}} \\ $$$${if}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mathrm{sin}\:{x}_{{i}} =\mathrm{0}. \\ $$ Commented by mr W…
Question Number 180894 by depressiveshrek last updated on 18/Nov/22 $${x}^{\mathrm{3}} +{x}=\mathrm{1} \\ $$$${x}^{\mathrm{8}} +\mathrm{3}{x}^{\mathrm{3}} =? \\ $$ Commented by Rasheed.Sindhi last updated on 19/Nov/22 $$\mathcal{T}{he}\:{solutions}/{answers}\:\left({complete}\right.…
Question Number 49823 by pieroo last updated on 11/Dec/18 $$\mathrm{Complete}\:\mathrm{the}\:\mathrm{square}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\mathrm{y}^{\mathrm{2}} +\mathrm{8y}+\mathrm{9k}\:\mathrm{and}\:\mathrm{hence}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{k}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{it}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$ Answered by ajfour last updated on 11/Dec/18 $$\left({y}+\mathrm{4}\right)^{\mathrm{2}}…
Question Number 180889 by mr W last updated on 18/Nov/22 $${the}\:{average}\:{of}\:\mathrm{10}\:{numbers}\:{is}\:\mathrm{5}.\:{the} \\ $$$${sum}\:{of}\:{their}\:{squares}\:{is}\:\mathrm{5000}.\:{how}\: \\ $$$${large}\:{can}\:{the}\:{largest}\:{number}\:{among} \\ $$$${them}\:{at}\:{most}\:{be}\:{and}\:{how}\:{small}\:{can}\: \\ $$$${the}\:{smallest}\:{number}\:{among}\:{them} \\ $$$${at}\:{most}\:{be}? \\ $$ Commented by…