Question Number 19409 by Tinkutara last updated on 10/Aug/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{squares}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:−\:\mathrm{7}\left[{x}\right]\:+\:\mathrm{5}\:=\:\mathrm{0}? \\ $$$$\left(\mathrm{Here}\:\left[{x}\right]\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\right. \\ $$$$\mathrm{less}\:\mathrm{than}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to}\:{x}.\:\mathrm{For}\:\mathrm{example} \\ $$$$\left.\left[\mathrm{3}.\mathrm{4}\right]\:=\:\mathrm{3}\:\mathrm{and}\:\left[−\mathrm{2}.\mathrm{3}\right]\:=\:−\mathrm{3}.\right) \\ $$ Commented by mrW1 last…
Question Number 19352 by Tinkutara last updated on 10/Aug/17 $$\mathrm{Prove}\:\mathrm{that}\:\mid{z}_{\mathrm{1}} \:−\:{z}_{\mathrm{2}} \mid^{\mathrm{2}} \:=\:\mid{z}_{\mathrm{1}} \mid^{\mathrm{2}} \:+\:\mid{z}_{\mathrm{2}} \mid^{\mathrm{2}} \\ $$$$−\:\mathrm{2}\mid{z}_{\mathrm{1}} \mid\:\mid{z}_{\mathrm{2}} \mid\:\mathrm{cos}\:\left(\theta_{\mathrm{1}} \:−\:\theta_{\mathrm{2}} \right) \\ $$ Answered…
Question Number 84778 by abdomathmax last updated on 16/Mar/20 $${let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}+{sinx}} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 150171 by puissant last updated on 10/Aug/21 $${solve}\:{in}\:\mathbb{R}: \\ $$$$\sqrt[{\mathrm{7}}]{\left({ax}−{b}\right)^{\mathrm{3}} }−\sqrt[{\mathrm{7}}]{\left({b}−{ax}\right)^{−\mathrm{3}} }=\frac{\mathrm{65}}{\mathrm{8}} \\ $$ Answered by liberty last updated on 10/Aug/21 $$\mathrm{let}\:\sqrt[{\mathrm{7}}]{\left(\mathrm{ax}−\mathrm{b}\right)^{\mathrm{3}} }\:=\:\mathrm{u}…
Question Number 84582 by jagoll last updated on 14/Mar/20 Commented by jagoll last updated on 14/Mar/20 $$\mathrm{dear}\:\mathrm{mr}\:\mathrm{W}.\:\mathrm{this}\:\mathrm{my}\:\mathrm{way}.\:\mathrm{it}'\mathrm{s} \\ $$$$\mathrm{correct}? \\ $$ Commented by jagoll last…
Question Number 84581 by msup trace by abdo last updated on 14/Mar/20 $${let}\:{f}\left({x}\right)\:=\:{e}^{\mathrm{2}{x}} {ln}\left(\mathrm{1}−\mathrm{3}{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left(\mathrm{0}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{drvelopp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int\:{f}\left({x}\right){dx} \\ $$…
Question Number 84576 by msup trace by abdo last updated on 14/Mar/20 $${find}\:{locus}\:{of}\:\:\:\mid{z}−\frac{\mathrm{1}}{{z}}\mid=\mathrm{2}\mid\overset{−} {{z}}\mid \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84579 by msup trace by abdo last updated on 14/Mar/20 $${find}\:\int\:\left({x}^{\mathrm{2}} −\mathrm{2}\right)\sqrt{{x}+\frac{\mathrm{1}}{{x}}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84575 by msup trace by abdo last updated on 14/Mar/20 $${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\Gamma\left(\frac{\mathrm{1}}{{n}}\right) \\ $$$$\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\:\:\:\:\left({x}>\mathrm{0}\right) \\ $$ Terms of…
Question Number 84572 by msup trace by abdo last updated on 14/Mar/20 $${let}\:\:{F}\left({z}\right)\:=\frac{{z}^{\mathrm{2}} }{\mathrm{1}+{z}^{\mathrm{7}} } \\ $$$$\left.\mathrm{1}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{and}\:{R}\left[{x}\right] \\ $$$${z}^{\mathrm{7}} \:+\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right) \\ $$$${the}\:{fraction}\:{F}\left({x}\right) \\…