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Category: Algebra

Question-188646

Question Number 188646 by Rupesh123 last updated on 04/Mar/23 Answered by Frix last updated on 04/Mar/23 $$\mathrm{Due}\:\mathrm{to}\:\mathrm{symmetry}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{of} \\ $$$$\left(\sqrt{{ab}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\sqrt{{ac}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\sqrt{{bc}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\:\mathrm{is}\:\mathrm{at} \\ $$$${c}={b}={a} \\ $$$$\Rightarrow \\ $$$$\mathrm{3}\sqrt{{a}}=\mathrm{2}{a}\sqrt{{a}}\:\Rightarrow\:{a}=\frac{\mathrm{3}}{\mathrm{2}}…

Question-123108

Question Number 123108 by benjo_mathlover last updated on 23/Nov/20 Commented by benjo_mathlover last updated on 23/Nov/20 $$\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}+\mathrm{3}\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{5}}+\mathrm{5}\sqrt{\mathrm{4}}}+ \\ $$$$…\:+\:\frac{\mathrm{1}}{\mathrm{4012008}\sqrt{\mathrm{4012009}}+\mathrm{4012009}\sqrt{\mathrm{4012008}}}\:? \\ $$ Commented by liberty last…

Erica-s-age-is-8-years-and-her-mother-is-42-In-how-many-years-time-will-the-mother-be-3-times-as-old-as-her-daughter-

Question Number 123062 by pete last updated on 22/Nov/20 $$\mathrm{Erica}'\mathrm{s}\:\mathrm{age}\:\mathrm{is}\:\mathrm{8}\:\mathrm{years}\:\mathrm{and}\:\mathrm{her}\:\mathrm{mother}\:\mathrm{is}\:\mathrm{42}. \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{years}\:\mathrm{time}\:\mathrm{will}\:\mathrm{the}\:\mathrm{mother}\:\mathrm{be} \\ $$$$\mathrm{3}\:\mathrm{times}\:\mathrm{as}\:\mathrm{old}\:\mathrm{as}\:\mathrm{her}\:\mathrm{daughter}? \\ $$ Answered by JDamian last updated on 22/Nov/20 $$\mathrm{42}+{y}=\mathrm{3}\left(\mathrm{8}+{y}\right) \\…

There-are-128-players-in-the-first-round-of-a-knockout-competition-Half-of-the-players-were-knocked-out-in-each-round-How-many-players-took-part-in-the-fourth-round-How-many-rounds-were-there-in-th

Question Number 57513 by pete last updated on 06/Apr/19 $$\mathrm{There}\:\mathrm{are}\:\mathrm{128}\:\mathrm{players}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{round} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{knockout}\:\mathrm{competition}.\:\mathrm{Half}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{players}\:\mathrm{were}\:\mathrm{knocked}\:\mathrm{out}\:\mathrm{in}\:\mathrm{each}\:\mathrm{round}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{players}\:\mathrm{took}\:\mathrm{part}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{fourth}\:\mathrm{round}?\:\mathrm{How}\:\mathrm{many}\:\mathrm{rounds}\:\mathrm{were}\:\mathrm{there} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{competion}? \\ $$ Commented by mr…