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Category: Algebra

What-is-the-smallest-even-number-greater-than-3-that-cannot-be-expressed-as-the-sum-of-two-prime-numbers-

Question Number 6772 by Tawakalitu. last updated on 24/Jul/16 $${What}\:{is}\:{the}\:{smallest}\:{even}\:{number}\:{greater}\:{than}\:\mathrm{3}\:{that}\:{cannot} \\ $$$${be}\:{expressed}\:{as}\:{the}\:{sum}\:{of}\:{two}\:{prime}\:{numbers}\:? \\ $$ Commented by Yozzii last updated on 24/Jul/16 $${Let}\:{S}\:{be}\:{a}\:{set}\:{of}\:{n}\:{elements},\:{so}\:{that}\:\mid{S}\mid={n}\geqslant\mathrm{4}. \\ $$$${Let}\:{P}\:{be}\:{a}\:{partition}\:{of}\:{S}\:{into}\:{two}\:{sets} \\…

Question-72291

Question Number 72291 by aliesam last updated on 27/Oct/19 Answered by mr W last updated on 27/Oct/19 $$\left(\mathrm{5}{m}\:\mathrm{sin}\:\left(\mathrm{3}{x}\right)\right)^{\mathrm{2}} =\left(\mathrm{4}\:\mathrm{sin}\:{x}\right)^{\mathrm{2}} \\ $$$$\mathrm{5}{m}\:\mathrm{sin}\:\left(\mathrm{3}{x}\right)=\pm\mathrm{4}\:\mathrm{sin}\:{x} \\ $$$$\mathrm{5}{m}\:\mathrm{sin}\:{x}\:\left(\mathrm{3}−\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:{x}\right)=\pm\mathrm{4}\:\mathrm{sin}\:{x} \\…

Question-137772

Question Number 137772 by peter frank last updated on 06/Apr/21 Answered by bemath last updated on 06/Apr/21 $$\Leftrightarrow\:\frac{\left(\mathrm{2}^{{n}} \right)^{\mathrm{3}} +\left(\mathrm{3}^{{n}} \right)^{\mathrm{3}} }{\left(\mathrm{2}^{{n}} \right)^{\mathrm{2}} \left(\mathrm{3}\right)^{{n}} +\mathrm{2}^{{n}}…

Solve-the-simultaneous-equation-x-y-y-x-17-equation-i-x-y-5-equation-ii-Please-help-

Question Number 6666 by Tawakalitu. last updated on 10/Jul/16 $${Solve}\:{the}\:{simultaneous}\:{equation}. \\ $$$$ \\ $$$${x}^{{y}} \:+\:{y}^{{x}} \:=\:\mathrm{17}\:\:\:………….\:{equation}\:\left({i}\right) \\ $$$${x}\:+\:{y}\:=\:\mathrm{5}\:\:\:………………\:{equation}\:\left({ii}\right) \\ $$$$ \\ $$$${Please}\:{help}\:!!! \\ $$ Commented…