Question Number 83512 by jagoll last updated on 03/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\frac{\mathrm{4x}^{\mathrm{2}} }{\left(\mathrm{1}−\sqrt{\mathrm{2x}+\mathrm{1}}\right)^{\mathrm{2}} }\:<\:\mathrm{2x}+\mathrm{9} \\ $$ Answered by john santu last updated on 03/Mar/20 $$\left(\mathrm{1}\right)\:\mathrm{2x}\:+\mathrm{9}\:>\:\mathrm{0}\:\Rightarrow\:\mathrm{x}\:>\:−\frac{\mathrm{9}}{\mathrm{2}}…
Question Number 149045 by mathdanisur last updated on 02/Aug/21 $$\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 149040 by mathdanisur last updated on 02/Aug/21 $$\begin{cases}{{x}^{\mathrm{2}} +{xy}=\mathrm{4}{x}}\\{{y}^{\mathrm{2}} +{xy}=\mathrm{4}{y}}\end{cases}\:\:\:\Rightarrow\:\:{log}_{\mathrm{16}} ^{\left(\boldsymbol{{x}}_{\mathrm{1}} +\boldsymbol{{y}}_{\mathrm{1}} +\boldsymbol{{x}}_{\mathrm{2}} +\boldsymbol{{y}}_{\mathrm{2}} \right)} \:=\:? \\ $$ Answered by bramlexs22 last updated…
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 149043 by Tawa11 last updated on 02/Aug/21 Commented by EDWIN88 last updated on 02/Aug/21 $${x}=\mathrm{2} \\ $$ Commented by Tawa11 last updated on…
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 $${p}^{\mathrm{3}}…
Question Number 149042 by mathdanisur last updated on 02/Aug/21 $$\mathrm{100}\boldsymbol{{x}}^{\boldsymbol{{lg}}\left(\boldsymbol{{x}}\right)} \:=\:\boldsymbol{{x}}^{\mathrm{3}} \:\:\:\Rightarrow\:\:\:\boldsymbol{{x}}\:=\:? \\ $$ Answered by bramlexs22 last updated on 02/Aug/21 $$\Rightarrow\mathrm{100x}^{\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{x}\right)} =\:\mathrm{x}^{\mathrm{3}} \\…
Question Number 149024 by mathdanisur last updated on 02/Aug/21 Answered by Olaf_Thorendsen last updated on 02/Aug/21 $${f}_{{n}} \left({x}\right)\:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{x}^{{k}} \:=\:{x}\frac{\mathrm{1}−{x}^{{n}} }{\mathrm{1}−{x}}\:=\:\frac{{x}−{x}^{{n}+\mathrm{1}} }{\mathrm{1}−{x}} \\ $$$${x}.{f}'\left({x}\right)\:=\:{x}\underset{{k}=\mathrm{1}}…
Question Number 149025 by mathdanisur last updated on 02/Aug/21 $${Solve}\:{for}\:{equation}: \\ $$$${cos}^{\mathrm{3}} \left({x}\right)\:-\:{sin}^{\mathrm{3}} \left({x}\right)\:+\:\mathrm{1} \\ $$ Commented by ArielVyny last updated on 02/Aug/21 $${equal}\:{what}??\:{the}\:{syntaxe}\:{is}\:{not}\:{correct}\:{sir} \\…
Question Number 83477 by M±th+et£s last updated on 02/Mar/20 $${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}…