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Author: Tinku Tara

find-the-cube-root-of-9ab-2-b-2-24a-2-b-2-3a-2-

Question Number 193221 by York12 last updated on 07/Jun/23 $$ \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{cube}}\:\boldsymbol{{root}}\:\boldsymbol{{of}} \\ $$$$\mathrm{9}\boldsymbol{{ab}}^{\mathrm{2}} \:+\:\left(\boldsymbol{{b}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{a}}^{\mathrm{2}} } \\ $$ Answered by som(math1967) last…

There-exists-a-unique-positive-integer-a-for-which-The-sum-u-n-1-2023-n-2-na-5-is-an-integer-strictly-between-1000-amp-1000-find-a-u-

Question Number 193183 by York12 last updated on 06/Jun/23 $$ \\ $$$${There}\:{exists}\:{a}\:{unique}\:{positive}\:{integer}\:{a}\:{for} \\ $$$${which}\:{The}\:{sum}\:{u}\:\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\lfloor\frac{{n}^{\mathrm{2}} −{na}}{\mathrm{5}}\rfloor\:{is}\:{an}\:{integer} \\ $$$${strictly}\:{between}\:−\mathrm{1000}\:\&\:\mathrm{1000}\:{find}\:{a}+{u}. \\ $$ Answered by York12 last…

x-2-2-2-1-2-y-2-2-2-3-2-z-2-2-2-5-2-w-2-2-2-7-2-1-x-2-4-2-1-2-y-2-4-2-3-2-z-2-4-2-5-2-w-2-4-2-7-2-1-x-2-6-2-1-2-y-2-6-2-3-2-z-2-

Question Number 193182 by York12 last updated on 06/Jun/23 $$ \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }+\frac{{w}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }=\mathrm{1} \\…

solve-7-x-2-

Question Number 193170 by aba last updated on 05/Jun/23 $$\mathrm{solve}\::\:\mathrm{7}^{\mathrm{x}} =−\mathrm{2} \\ $$ Answered by Frix last updated on 06/Jun/23 $$−\mathrm{2}=\mathrm{2e}^{\mathrm{i}\pi\left(\mathrm{2}{n}+\mathrm{1}\right)} \forall{n}\in\mathbb{Z} \\ $$$$\mathrm{7}^{{x}} =\mathrm{2e}^{\mathrm{i}\pi\left(\mathrm{2}{n}+\mathrm{1}\right)}…