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Category: Algebra

x-1-5-2-has-solution-set-is-a-x-b-or-x-c-x-d-Find-a-d-b-c-

Question Number 162715 by tounghoungko last updated on 31/Dec/21 $$\:\:\:\mid\mid{x}−\mathrm{1}\mid−\mathrm{5}\mid\:\geqslant\:\mathrm{2}\:\:{has}\:{solution}\:{set} \\ $$$$\:{is}\:{a}\:\leqslant{x}\leqslant{b}\:{or}\:{x}\leqslant\:{c}\:\cup\:{x}\geqslant{d}\:. \\ $$$$\:{Find}\:\frac{{a}+{d}}{{b}+{c}}\:. \\ $$ Answered by bobhans last updated on 01/Jan/22 $$\:\mid\mid\mathrm{x}−\mathrm{1}\mid−\mathrm{5}\mid\:\geqslant\mathrm{2}\:\Rightarrow\:\left(\mid\mathrm{x}−\mathrm{1}\mid−\mathrm{7}\right)\left(\mid\mathrm{x}−\mathrm{1}\mid−\mathrm{3}\right)\geqslant\mathrm{0} \\…

prove-that-sin-16x-cot-x-1-2cos-2x-2cos-4x-2cos-6x-2cos-16x-

Question Number 97135 by  M±th+et+s last updated on 06/Jun/20 $${prove}\:{that}: \\ $$$${sin}\left(\mathrm{16}{x}\right)\:{cot}\left({x}\right)=\mathrm{1}+\mathrm{2}{cos}\left(\mathrm{2}{x}\right)+\mathrm{2}{cos}\left(\mathrm{4}{x}\right)+\mathrm{2}{cos}\left(\mathrm{6}{x}\right)+…+\mathrm{2}{cos}\left(\mathrm{16}{x}\right) \\ $$ Commented by prakash jain last updated on 07/Jun/20 $$\mathrm{cos}\:{x}=\frac{\mathrm{1}}{\mathrm{2}}\left({e}^{{ix}} +{e}^{−{ix}} \right)…

Question-31594

Question Number 31594 by Nayon.Sm last updated on 11/Mar/18 Answered by Rasheed.Sindhi last updated on 11/Mar/18 $${a}=\mathrm{0}\:\mid\:{b}=\mathrm{0}\:;\:\mathrm{No}\:\mathrm{other}\:\mathrm{integral}\:\mathrm{solution}. \\ $$$$−.−.−.−.−.−.− \\ $$$$\mathrm{If}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \:\mathrm{then}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{integers} \\…