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Category: Algebra

Question-80209

Question Number 80209 by peter frank last updated on 01/Feb/20 Commented by mathmax by abdo last updated on 01/Feb/20 $${z}+\frac{\mathrm{1}}{{z}}\:=−\mathrm{1}\:\Rightarrow{z}^{\mathrm{2}} \:+\mathrm{1}=−{z}\:\Rightarrow{z}^{\mathrm{2}} \:+{z}+\mathrm{1}=\mathrm{0} \\ $$$$\Delta=\mathrm{1}−\mathrm{4}=−\mathrm{3}\:\Rightarrow{z}_{\mathrm{1}} =\frac{−\mathrm{1}+{i}\sqrt{\mathrm{3}}}{\mathrm{2}}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}}…

Question-80204

Question Number 80204 by jagoll last updated on 01/Feb/20 Commented by Tony Lin last updated on 01/Feb/20 $$\mathrm{28}\left({x}+{y}+{z}\right)=\mathrm{363}+\left({x}−{z}\right) \\ $$$${if}\:{x}+{y}+{z}\geqslant\mathrm{14} \\ $$$${x}−{z}\geqslant\mathrm{29}>{x}+{y}+{z}\left({false}\right) \\ $$$${if}\:{x}+{y}+{z}=\mathrm{13} \\…

Question-80178

Question Number 80178 by Power last updated on 31/Jan/20 Commented by mr W last updated on 31/Jan/20 $${no}\:{exact}\:{value}\:{possible}! \\ $$$${x}^{\mathrm{25}} \underset{{k}=\mathrm{1}} {\overset{\mathrm{25}} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{{k}} }\right)=\mathrm{1} \\…