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Category: Algebra

Find-0-x-ln-x-x-2-1-dx-

Question Number 155479 by mathdanisur last updated on 01/Oct/21 $$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\sqrt{\mathrm{x}}\:\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$ Commented by mathdanisur last updated on 01/Oct/21 $$\mathrm{Very}\:\mathrm{nice}\:\mathrm{solution},\:\mathrm{thank}\:\mathrm{you}\:\boldsymbol{\mathrm{S}}\mathrm{er} \\ $$…

If-x-x-1-1-find-x-1-3-1-x-1-3-

Question Number 89938 by jagoll last updated on 20/Apr/20 $$\mathrm{If}\:\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{1}\: \\ $$$$\mathrm{find}\:\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} −\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Commented by john santu last updated on 20/Apr/20 $${let}\:{x}+\mathrm{1}=\:{t}\:\Rightarrow{x}\:=\:{t}−\mathrm{1}…

x-1-1-1-1-x-and-y-2-2-1-1-y-find-x-y-

Question Number 89920 by akash4081 last updated on 20/Apr/20 $${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+{x}}}\:{and}\:{y}=\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{1}+{y}\:}}\:{find}\:{x}+{y} \\ $$ Commented by john santu last updated on 20/Apr/20 $${x}\:=\:\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\:\Rightarrow\:{x}\:=\:\frac{−\mathrm{1}\:\pm\:\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${y}\:=\:\frac{\mathrm{2}\left({y}+\mathrm{1}\right)}{\mathrm{2}{y}+\mathrm{3}}\:\Rightarrow\:{y}\:=\:\frac{−\mathrm{1}\:\pm\:\sqrt{\mathrm{17}}}{\mathrm{4}} \\ $$$$\therefore\:{x}+{y}\:=\:\left(\frac{−\mathrm{1}\pm\sqrt{\mathrm{5}}}{\mathrm{2}}\right)+\left(\frac{−\mathrm{1}\pm\sqrt{\mathrm{17}}}{\mathrm{4}}\right)…

S-m-0-1-n-0-m-10-n-m-

Question Number 155436 by talminator2856791 last updated on 03/Oct/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{S}\:=\:\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\underset{{n}=\mathrm{0}} {\overset{{m}} {\sum}}\:\mathrm{10}^{{n}} +\:{m}} \\ $$$$\: \\ $$ Terms of Service Privacy…

If-the-sum-of-4-numbers-is-between-53-and-57-then-the-arithmetic-mean-of-the-numbers-could-be-one-of-the-following-a-11-5-b-12-c-12-5-d-13-e-14-

Question Number 89907 by necxxx last updated on 19/Apr/20 $${If}\:{the}\:{sum}\:{of}\:\mathrm{4}\:{numbers}\:{is}\:{between} \\ $$$$\mathrm{53}\:{and}\:\mathrm{57}\:{then}\:{the}\:{arithmetic}\:{mean}\:{of} \\ $$$${the}\:{numbers}\:{could}\:{be}\:{one}\:{of}\:{the} \\ $$$${following} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{1}\left..\mathrm{5}\:{b}\right)\mathrm{12}\:{c}\right)\mathrm{12}.\mathrm{5}\:{d}\right)\mathrm{13}\:{e}\right)\mathrm{14} \\ $$ Answered by MJS…