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Category: Algebra

7-2-7-2-7-2-7-2-7-

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Question Number 100193 by bobhans last updated on 25/Jun/20 $$\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+\mathrm{2}\sqrt{\mathrm{7}−\mathrm{2}\sqrt{\mathrm{7}+…}}}}}\:? \\ $$ Commented by bobhans last updated on 25/Jun/20 $${x}\:=\sqrt{\mathrm{7}+\mathrm{2}{y}}\:;\:\mathrm{y}=\sqrt{\mathrm{7}−\mathrm{2}{x}} \\ $$$$\Leftrightarrow{x}^{\mathrm{2}} \:=\:\mathrm{7}+\mathrm{2}{y}\:\_\left(\mathrm{1}\right) \\ $$$$\Leftrightarrow\mathrm{y}^{\mathrm{2}}…

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Question Number 34606 by abdo mathsup 649 cc last updated on 08/May/18 $${let}\:{give}\:{p}\left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} \:−\left({x}−\mathrm{1}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\prod_{{k}=\mathrm{1}} ^{{p}} \:\:{cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right) \\ $$ Terms of Service…

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Question Number 34607 by abdo mathsup 649 cc last updated on 08/May/18 $${let}\:{p}\in{C}\left[{x}\right]\:{degp}={n}\:\:\:\left({x}_{{i}} \right)_{\mathrm{1}\leqslant{k}\leqslant{n}} {the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$${a}\in{C}?/{p}\left({a}\right)\neq\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{S}_{\mathrm{1}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{x}_{{k}} −{a}}\:{interms}\:{of}\:{p},{p}^{'} \:{and}\:{a} \\…

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