Category: Algebra

Question Number 203245 by hardmath last updated on 13/Jan/24 $$\mathrm{If}\:\:\:\mathrm{x}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{2019}}\:+\:\mathrm{1} \\ $$$$\mathrm{Find}: \\ $$$$\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{3}} −\mathrm{6}\centerdot\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} \:+\:\mathrm{12x}\:−\:\mathrm{3} \\ $$ Answered by mr W last updated on…

Question Number 203275 by Frix last updated on 13/Jan/24 $$\mathrm{Show}\:\mathrm{this}\:\mathrm{has}\:\mathrm{exactly}\:\mathrm{7}\:\mathrm{solutions}\:\mathrm{for}\:{x}\in\mathbb{C}: \\ $$$${x}^{\mathrm{ln}\:{x}} =\mathrm{1} \\ $$ Commented by aleks041103 last updated on 14/Jan/24 $${When}\:{you}\:{use}\:{ln}\left({x}\right)\:{do}\:{you}\:{imply}\:{the}\:{principle} \\ $$$${branch}\:{of}\:{this}\:{function}?…

Question Number 203222 by Tawa11 last updated on 12/Jan/24 XYZ Ltd wants to borrow money to finance a project. They can pay N2500 monthly in…

Question Number 203219 by hardmath last updated on 12/Jan/24 Answered by witcher3 last updated on 15/Jan/24 $$\mathrm{evident} \\ $$$$\left(\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\right)^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} +\mathrm{2}\left(\mathrm{ab}+\mathrm{bc}+\mathrm{cd}+\mathrm{da}\right) \\…

Question Number 203206 by hardmath last updated on 12/Jan/24 Answered by mr W last updated on 12/Jan/24 $$\underset{{k}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mid{i}−{k}\mid \\ $$$$=\underset{{k}=\mathrm{1}} {\overset{{i}} {\sum}}\mid{i}−{k}\mid+\underset{{k}={i}+\mathrm{1}} {\overset{\mathrm{100}}…