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Category: Algebra

prove-that-log-2-2-2-n-1-n-n-1-2-2-n-log-2-n-1-n-n-1-3-2-n-n-1-n-n-1-4-2-n-23-8-6-2-2-3-1-18-log-6-2-m-A-

Question Number 155136 by amin96 last updated on 25/Sep/21 $$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\frac{\boldsymbol{\mathrm{log}}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}}\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left(\boldsymbol{{n}}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{2}} \mathrm{2}^{\boldsymbol{{n}}} }+\boldsymbol{\mathrm{log}}\left(\mathrm{2}\right)\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left({n}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{3}} \mathrm{2}^{\boldsymbol{{n}}} }+\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\varphi}\left({n}\right)}{\left(\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{4}} \mathrm{2}^{\boldsymbol{{n}}} }=…

Solve-for-real-numbers-x-y-x-y-x-2-y-2-5-2x-3-x-2-y-2-19-

Question Number 155106 by mathdanisur last updated on 25/Sep/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}+\mathrm{y}}\:-\:\sqrt{\mathrm{x}-\mathrm{y}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{5}}\\{\mathrm{2x}\:+\:\mathrm{3}\sqrt{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{19}}\end{cases} \\ $$ Commented by benhamimed last updated on 25/Sep/21…

Determine-all-triangle-with-1-The-lengths-of-sides-positive-integers-and-at-least-one-is-prime-number-2-The-semiperimetr-is-positive-integer-and-area-is-equal-with-perimetr-

Question Number 155100 by mathdanisur last updated on 25/Sep/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{triangle}\:\mathrm{with}: \\ $$$$\mathrm{1}.\mathrm{The}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{is}\:\mathrm{prime}\:\mathrm{number}. \\ $$$$\mathrm{2}.\mathrm{The}\:\mathrm{semiperimetr}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{area}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{with}\:\mathrm{perimetr}. \\ $$ Commented by MJS_new last updated…

Question-155083

Question Number 155083 by Tawa11 last updated on 25/Sep/21 Answered by physicstutes last updated on 25/Sep/21 $$\left(\mathrm{a}\right)\:{f}\left({x}\right)=\:\frac{\mathrm{2}}{{x}^{\mathrm{2}} }\:,\:{x}\:\neq\mathrm{0} \\ $$$${f}\left({x}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{differentiable}\:\mathrm{on}\:−\mathrm{1}<{x}<\mathrm{1} \\ $$$$\left(\mathrm{b}\right)\:{g}\left({x}\right)=\mid{x}\mid\:\mathrm{is}\:\mathrm{not}\:\mathrm{differentiable}\:\mathrm{on} \\ $$$$−\mathrm{1}<{x}<\mathrm{1} \\…