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Author: Tinku Tara

Question-137111

Question Number 137111 by mnjuly1970 last updated on 29/Mar/21 Answered by Dwaipayan Shikari last updated on 29/Mar/21 $$\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{1}}=\mathrm{1}+\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{1}}=\mathrm{1}+\frac{\mathrm{2}}{\mathrm{2}}\left(\pi{coth}\left(\pi\right)−\mathrm{1}\right)=\pi\frac{{e}^{\mathrm{2}\pi} +\mathrm{1}}{{e}^{\mathrm{2}\pi}…

Solve-2x-x-2-y-2-1-x-y-2y-0-Given-y-x-2-is-a-solution-

Question Number 71570 by TawaTawa last updated on 17/Oct/19 $$\mathrm{Solve}:\:\:\:\:\:\left(\mathrm{2x}\:+\:\mathrm{x}^{\mathrm{2}} \right)\mathrm{y}''\:−\:\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{x}\right)\mathrm{y}'\:+\:\mathrm{2y}\:\:=\:\:\mathrm{0} \\ $$$$\mathrm{Given}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}. \\ $$ Answered by mind is power last updated on 17/Oct/19…

Solve-3cos5x-4sin4x-3-0-in-R-

Question Number 137103 by Boucatchou last updated on 29/Mar/21 $$\:\:\:\:\:\:\:\:\:{Solve}\:\:\mathrm{3}{cos}\mathrm{5}{x}−\mathrm{4}{sin}\mathrm{4}{x}−\mathrm{3}=\mathrm{0}\:\:{in}\:\mathbb{R} \\ $$ Answered by MJS_new last updated on 30/Mar/21 $$\mathrm{obviously}\:{x}=\mathrm{2}{n}\pi\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution} \\ $$$$\mathrm{the}\:\mathrm{others}\:\mathrm{can}\:\mathrm{only}\:\mathrm{be}\:\mathrm{approximated} \\ $$$${x}\approx.\mathrm{966119}+\mathrm{2}{n}\pi \\…

z-i-4-7-24i-

Question Number 71564 by 20190927 last updated on 17/Oct/19 $$\left(\mathrm{z}−\mathrm{i}\right)^{\mathrm{4}} =−\mathrm{7}+\mathrm{24i} \\ $$ Commented by mathmax by abdo last updated on 18/Oct/19 $${we}\:{have}\:\mid−\mathrm{7}+\mathrm{24}{i}\mid=\sqrt{\mathrm{7}^{\mathrm{2}} \:+\mathrm{24}^{\mathrm{2}} }=\sqrt{\mathrm{49}+\mathrm{576}}=\sqrt{\mathrm{625}}=\mathrm{25}\:\Rightarrow…