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Category: Algebra

Question-109626

Question Number 109626 by qwerty111 last updated on 24/Aug/20 Commented by kaivan.ahmadi last updated on 24/Aug/20 $${log}_{\mathrm{20}} \mathrm{2}×\mathrm{5}^{\mathrm{3}} ={log}_{\mathrm{20}} \mathrm{2}+\mathrm{3}{log}_{\mathrm{20}} \mathrm{5}=\frac{\mathrm{1}}{{log}_{\mathrm{2}} \mathrm{20}}+\frac{\mathrm{3}}{{log}_{\mathrm{5}} \mathrm{20}}= \\ $$$$\frac{\mathrm{1}}{\mathrm{2}+{log}_{\mathrm{2}}…

sin-2-2sin-cos-2-1-cos-cos2-cos3-

Question Number 109625 by qwerty111 last updated on 24/Aug/20 $$\frac{\mathrm{sin}\:\mathrm{2}\boldsymbol{\alpha}+\mathrm{2sin}\:\boldsymbol{\alpha}\centerdot\mathrm{cos}\:\mathrm{2}\boldsymbol{\alpha}}{\mathrm{1}+\mathrm{cos}\:\boldsymbol{\alpha}+\mathrm{cos2}\:\boldsymbol{\alpha}+\mathrm{cos3}\:\boldsymbol{\alpha}} \\ $$ Commented by nimnim last updated on 24/Aug/20 $${tan}\alpha \\ $$ Commented by kaivan.ahmadi…

Question-175148

Question Number 175148 by Shrinava last updated on 20/Aug/22 Commented by mr W last updated on 21/Aug/22 $${wrong}! \\ $$$${for}\:{a}=−\mathrm{1},\:{b}=\mathrm{1} \\ $$$$\mathrm{2}^{{b}} −\mathrm{2}^{{a}} =\mathrm{2}−\frac{\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{2}}=\mathrm{1}.\mathrm{5}>\frac{\mathrm{9}\:\mathrm{log}\:\mathrm{2}}{\mathrm{4}}\approx\mathrm{0}.\mathrm{677} \\…

Question-109611

Question Number 109611 by mnjuly1970 last updated on 24/Aug/20 Commented by Rasheed.Sindhi last updated on 25/Aug/20 $$\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{3}} =\left({x}^{\mathrm{2}} \right)^{\mathrm{3}} +\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \right)^{\mathrm{3}} }+\mathrm{3}\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}}…

Question-44062

Question Number 44062 by peter frank last updated on 20/Sep/18 Answered by MJS last updated on 21/Sep/18 $$\mathrm{roots}\:{r}_{\mathrm{1}} ,\:{r}_{\mathrm{2}} \:\Rightarrow\:\left({x}−{r}_{\mathrm{1}} \right)\left({x}−{r}_{\mathrm{2}} \right)=\mathrm{0}\:\Rightarrow\:{x}^{\mathrm{2}} −\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right){x}+{r}_{\mathrm{1}}…

Question-algebra-Count-the-number-of-zero-divisor-of-ring-Z-45-m-n-

Question Number 175132 by mnjuly1970 last updated on 20/Aug/22 $$ \\ $$$$\:\:\:\:\:\:\prec\:\:\boldsymbol{{Question}}−\:\boldsymbol{{algebra}}\:\succ \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{{Count}}\:\boldsymbol{{the}}\:\boldsymbol{{number}}\:\boldsymbol{{of}}\:\:\:''\:\boldsymbol{{zero}}\:\boldsymbol{{divisor}}\:'' \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{{of}}\:\:\boldsymbol{{ring}}\:,\:\:\:\left(\:\mathbb{Z}_{\:\mathrm{45}} \:,\: \:,\:\oplus\:\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:\boldsymbol{{m}}.\boldsymbol{{n}}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−\:\:\:\: \\ $$ Commented…

For-any-Real-numbers-x-y-and-z-if-x-y-z-2-then-prove-that-xyz-8-1-x-1-y-1-z-

Question Number 109595 by nimnim last updated on 24/Aug/20 $${For}\:{any}\:{Real}\:{numbers}\:{x},{y}\:{and}\:{z}, \\ $$$$\:{if}\:\:\left({x}+{y}+{z}\right)=\mathrm{2},\:{then}\:{prove}\:{that} \\ $$$$\:\:\:\:\:\:\:\:{xyz}\geqslant\mathrm{8}\left(\mathrm{1}−{x}\right)\left(\mathrm{1}−{y}\right)\left(\mathrm{1}−{z}\right) \\ $$ Commented by 1549442205PVT last updated on 25/Aug/20 $$\mathrm{This}\:\mathrm{inequality}\:\mathrm{is}\:\mathrm{only}\:\mathrm{true}\:\mathrm{for} \\…

Question-175121

Question Number 175121 by Michaelfaraday last updated on 20/Aug/22 Answered by BaliramKumar last updated on 20/Aug/22 $$\left(\mathrm{3}^{−\mathrm{1}} \right)^{\frac{{x}^{\mathrm{2}} −\mathrm{2}{x}}{\mathrm{16}−\mathrm{2}{x}^{\mathrm{3}} }} \:=\:\left(\mathrm{3}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{4}{x}}} \\ $$$$\mathrm{3}^{\left(\frac{{x}^{\mathrm{2}} −\mathrm{2}{x}}{\mathrm{2}{x}^{\mathrm{3}}…