Category: Algebra

Question Number 149045 by mathdanisur last updated on 02/Aug/21 $$\mid\overset{\rightarrow} {\boldsymbol{{a}}}\mid\:=\:\mid\overset{\rightarrow} {\boldsymbol{{b}}}\mid\:=\:\mathrm{4}\:\:\:{and}\:\:\:{cos}\boldsymbol{\alpha}\:=\:\mathrm{60}° \\ $$$${find}\:\:\:\overset{\rightarrow} {\boldsymbol{{a}}}\:\centerdot\:\overset{\rightarrow} {\boldsymbol{{b}}}\:=\:? \\ $$ Answered by puissant last updated on 02/Aug/21…

Question Number 149041 by mathdanisur last updated on 02/Aug/21 $$\sqrt{{x}\:-\:\mathrm{3}\:+\:\mathrm{2}\sqrt{{x}\:-\:\mathrm{4}}}\:−\:\sqrt{{x}\:+\:\mathrm{5}\:-\:\mathrm{6}\sqrt{{x}\:-\:\mathrm{2}}}\:=\mathrm{2} \\ $$$$\Rightarrow\:\boldsymbol{{x}}\:=\:? \\ $$ Commented by bramlexs22 last updated on 02/Aug/21 Commented by MJS_new last…

Question Number 149036 by mathdanisur last updated on 02/Aug/21 $${if}\:\:\:{x};{y};{z}>\mathrm{0}\:\:\:{and}\:\:\:{xyz}=\mathrm{8}\:\:\:{prove}\:{that}: \\ $$$$\frac{\mathrm{1}}{{x}^{\mathrm{2}} \:+\:\mathrm{8}}\:+\:\frac{\mathrm{1}}{{y}^{\mathrm{2}} \:+\:\mathrm{8}}\:+\:\frac{\mathrm{1}}{{z}^{\mathrm{2}} \:+\:\mathrm{8}}\:\leqslant\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Answered by dumitrel last updated on 02/Aug/21 $${p}^{\mathrm{3}}…

Question Number 149024 by mathdanisur last updated on 02/Aug/21 Answered by Olaf_Thorendsen last updated on 02/Aug/21 $${f}_{{n}} \left({x}\right)\:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{x}^{{k}} \:=\:{x}\frac{\mathrm{1}−{x}^{{n}} }{\mathrm{1}−{x}}\:=\:\frac{{x}−{x}^{{n}+\mathrm{1}} }{\mathrm{1}−{x}} \\ $$$${x}.{f}'\left({x}\right)\:=\:{x}\underset{{k}=\mathrm{1}}…

Question Number 83477 by M±th+et£s last updated on 02/Mar/20 $${a}^{{b}} +{b}^{{a}} =\mathrm{1}\:\:\:{a}=?\:,\:{b}=? \\ $$$${a}\neq{b}\neq\mathrm{0} \\ $$ Commented by mr W last updated on 03/Mar/20 $${if}\:{a},{b}\in{R},\:{then}\:{i}\:{think}\:{there}\:{is}\:{no}…