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Category: Algebra

Question-188647

Question Number 188647 by Rupesh123 last updated on 04/Mar/23 Commented by mr W last updated on 05/Mar/23 $$\mathrm{4}. \\ $$$$\underset{{max}} {\mathrm{3}}^{\:\:\:\frac{\mathrm{1}}{\mathrm{3}}} >\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{4}^{\frac{\mathrm{1}}{\mathrm{4}}} >\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{5}}} >\mathrm{6}^{\frac{\mathrm{1}}{\mathrm{6}}}…

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) \\…