Question Number 65227 by Tawa1 last updated on 26/Jul/19 Commented by Tony Lin last updated on 26/Jul/19 $${let}\:\alpha,\beta\:{two}\:{roots}\:{of}\:{x}^{\mathrm{2}} +{ax}+\mathrm{1}=\mathrm{0} \\ $$$$\alpha\beta=\mathrm{1}\:{and}\:\alpha,\beta\:{are}\:{integers} \\ $$$$\left({irrational}\:{roots}\:{come}\:{in}\:{pair}\:{if}\:{the}\right. \\ $$$${coefficient}\:{of}\:{polynomial}\:{equation}…
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Question Number 130759 by mnjuly1970 last updated on 28/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}\:… \\ $$$$\:{find}\::\:\phi\:=\int_{\mathrm{0}} ^{\:\infty} \left({x}^{\mathrm{2}} {ln}\left(\mathrm{1}+{e}^{{x}} \right)−{x}^{\mathrm{3}} \right){dx} \\ $$$$ \\ $$ Answered by mnjuly1970 last…
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Question Number 65219 by Rio Michael last updated on 26/Jul/19 Commented by Rio Michael last updated on 26/Jul/19 $${please}\:{check}\:{my}\:{solution}\:{and}\:{correct}\:{me}\:{for}\:{that}\:{question} \\ $$$${you}\:{can}\:{give}\:{new}\:{methods}\:{to}\:{solve}\:{please}. \\ $$ Answered by…
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Question Number 65217 by Tanmay chaudhury last updated on 26/Jul/19 Commented by peter frank last updated on 26/Jul/19 $${nice} \\ $$ Terms of Service Privacy…
Question Number 130753 by Algoritm last updated on 28/Jan/21 Answered by Dwaipayan Shikari last updated on 28/Jan/21 $$\left.{a}\right)\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2}{n}−\mathrm{1}}{\mathrm{2}^{{n}−\mathrm{1}} }=\mathrm{4}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{\mathrm{2}^{{n}} }−\overset{\infty} {\sum}\frac{\mathrm{1}}{\mathrm{2}^{{n}−\mathrm{1}}…