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Category: Algebra

Question-170832

Question Number 170832 by Shrinava last updated on 01/Jun/22 Commented by mr W last updated on 01/Jun/22 $${T}={AM}+{BN}\geqslant\sqrt{{AB}^{\mathrm{2}} +{MN}^{\mathrm{2}} }=\sqrt{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }=\sqrt{\mathrm{34}} \\…

Question-170738

Question Number 170738 by Tawa11 last updated on 30/May/22 Commented by Tawa11 last updated on 30/May/22 $$\mathrm{How}\:\mathrm{to}\:\mathrm{get}\:\mathrm{the}\:\mathrm{second}\:\mathrm{step}\:\mathrm{please}???? \\ $$$$\mathrm{S}\:\:\:=\:\:\:\frac{\mathrm{1}}{\mathrm{8}}\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{3}}{\left(\mathrm{3n}\:+\:\mathrm{1}\right)\left(\mathrm{3n}\:+\:\mathrm{2}\right)}\:\:−\:\:\frac{\mathrm{5}}{\left(\mathrm{3n}\:+\:\mathrm{2}\right)\left(\mathrm{3n}\:+\:\mathrm{3}\right)}\:\:+\:\:\frac{\mathrm{2}}{\left(\mathrm{3n}\:+\:\mathrm{3}\right)\left(\mathrm{3n}\:+\:\mathrm{1}\right)} \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{question}\:… \\ $$…

Question-170729

Question Number 170729 by solomonwells last updated on 30/May/22 Commented by phamkhanhhuong last updated on 30/May/22 $$\Leftrightarrow\sqrt{{x}−\mathrm{1}+\mathrm{2}\sqrt{{x}−\mathrm{1}}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}−\mathrm{2}\sqrt{{x}−\mathrm{1}}+\mathrm{1}}={x}−\mathrm{1} \\ $$$$\Leftrightarrow\sqrt{\left(\sqrt{{x}−\mathrm{1}}+\mathrm{1}\right)^{\mathrm{2}} }+\sqrt{\left(\sqrt{{x}−\mathrm{1}}−\mathrm{1}\right)^{\mathrm{2}} }={x}−\mathrm{1} \\ $$$$\Leftrightarrow\mid\sqrt{{x}−\mathrm{1}}+\mathrm{1}\mid+\mid\sqrt{{x}−\mathrm{1}}−\mathrm{1}\mid={x}−\mathrm{1}\left(\ast\right) \\ $$$$\sqrt{{x}−\mathrm{1}}+\mathrm{1}>\mathrm{0}\:\forall{x}\in\left[\mathrm{1};+\infty\right).…

Question-105189

Question Number 105189 by qwertyu last updated on 26/Jul/20 Commented by floor(10²Eta[1]) last updated on 26/Jul/20 $$\mathrm{hey}\:\mathrm{chill}\:\mathrm{out}\:\mathrm{man}\:\mathrm{you}\:\mathrm{don}'\mathrm{t}\:\mathrm{need}\:\mathrm{to} \\ $$$$\mathrm{care}\:\mathrm{about}\:\mathrm{this}\:\mathrm{guy},\:\mathrm{we}\:\mathrm{still}\:\mathrm{need}\:\mathrm{you}\:\mathrm{to} \\ $$$$\mathrm{help}\:\mathrm{us}\:\mathrm{in}\:\mathrm{the}\:\mathrm{forum}.\: \\ $$$$ \\ $$$$…

Question-39639

Question Number 39639 by jasno91 last updated on 09/Jul/18 Answered by $@ty@m last updated on 09/Jul/18 $${length}\:{of}\:{lace}=\mathrm{2}\left(\mathrm{2}.\mathrm{25}+\mathrm{1}.\mathrm{75}\right) \\ $$$$=\mathrm{8}{m} \\ $$$${cost}=\mathrm{8}×\mathrm{14}.\mathrm{50} \\ $$$$={Rs}.\:\mathrm{116} \\ $$…

let-P-x-x-3-2-x-3-1-determine-the-roots-of-P-2-determine-the-roots-of-P-1-

Question Number 39636 by math khazana by abdo last updated on 09/Jul/18 $${let}\:{P}_{\alpha} \left({x}\right)\:={x}^{\mathrm{3}} \:\:+\mathrm{2}\alpha\:{x}\:−\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{P}_{\alpha} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{the}\:{roots}\:{of}\:\:{P}_{−\mathrm{1}} \\ $$ Answered by ajfour last…