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Category: Algebra

Dertermine-all-pairs-x-y-of-integers-such-that-2010x-xy-2012y-1-0-

Question Number 159863 by HongKing last updated on 21/Nov/21 $$\mathrm{Dertermine}\:\mathrm{all}\:\mathrm{pairs}\:\left(\boldsymbol{\mathrm{x}};\boldsymbol{\mathrm{y}}\right)\:\mathrm{of}\:\mathrm{integers} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{2010x}\:-\:\mathrm{xy}\:+\:\mathrm{2012y}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$ Answered by mr W last updated on 21/Nov/21 $$\left({x}−\mathrm{2012}\right){y}=\mathrm{1}+\mathrm{2010}{x}…

Question-159860

Question Number 159860 by Khalmohmmad last updated on 21/Nov/21 Commented by MJS_new last updated on 22/Nov/21 $${t}+{t}^{−\mathrm{1}} =−\mathrm{1} \\ $$$${t}^{\mathrm{2}} +{t}+\mathrm{1}=\mathrm{0}\:\Rightarrow\:\mathrm{no}\:\mathrm{real}\:\mathrm{solution} \\ $$$${t}=−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i} \\ $$$${t}^{\mathrm{1402}}…