Question Number 48208 by naka3546 last updated on 20/Nov/18 $${f}\left({x}\right)\:+\:\left({x}\:+\:\mathrm{1}\right)^{\mathrm{3}} \:\:=\:\:\mathrm{2}{f}\left({x}\:+\:\mathrm{1}\right) \\ $$$${f}\left(\mathrm{10}\right)\:\:=\:\:? \\ $$ Answered by MJS last updated on 20/Nov/18 $${f}\left({x}\right)={ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}…
Question Number 179266 by mokys last updated on 27/Oct/22 $${prove}\:{that}\:\mid{z}−{w}\mid^{\mathrm{2}} +\mid{z}\:−\:\overset{−} {{w}}\mid\:=\:\mathrm{4}\:{R}\boldsymbol{{e}}\:{z}\:{Rew} \\ $$ Commented by mokys last updated on 27/Oct/22 $$\bigstar \\ $$$$ \\…
Question Number 113714 by mathdave last updated on 14/Sep/20 Answered by Olaf last updated on 15/Sep/20 $$\mathrm{I}_{{n}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} \mathrm{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}}{dx} \\ $$$$\mathrm{I}_{\mathrm{0}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 113708 by Rasikh last updated on 15/Sep/20 $$\:\:\:\:\:\int\mathrm{x}^{\mathrm{x}} \:\mathrm{dx}\:=?\:\: \\ $$ Commented by Dwaipayan Shikari last updated on 14/Sep/20 $${Q}\:\mathrm{111558} \\ $$ Answered…
Question Number 113706 by Rasikh last updated on 15/Sep/20 $$\:\:\:\int\sqrt{\mathrm{tanx}}\:\mathrm{dx}\:=?\:\:\:\: \\ $$ Answered by MJS_new last updated on 15/Sep/20 $$\int\sqrt{\mathrm{tan}\:{x}}\:{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\mathrm{2cos}^{\mathrm{2}} \:{x}\:\sqrt{\mathrm{tan}\:{x}}\:{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}}…
Question Number 179228 by mahdipoor last updated on 26/Oct/22 $${prove}\:{in}\:{right}\:{triangle}\::\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \\ $$$$−−−−−− \\ $$ Answered by a.lgnaoui last updated on 27/Oct/22 $${Aire}\:\left({S}\right){du}\:{trapeze}\left[\mathrm{ADEB}\right] \\…
Question Number 179229 by mokys last updated on 26/Oct/22 Answered by 123564 last updated on 01/Nov/22 Commented by 123564 last updated on 01/Nov/22 Commented by…
Question Number 113684 by ZiYangLee last updated on 14/Sep/20 $$\mathrm{A}\:\mathrm{nice}\:\mathrm{question}\:<\mathrm{3} \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$$\left(\mathrm{1}−{q}+\frac{{p}^{\mathrm{2}} }{\mathrm{2}}\right){x}^{\mathrm{2}} +{p}\left(\mathrm{1}+{q}\right){x}+{q}\left({q}−\mathrm{1}\right)+\frac{{p}^{\mathrm{2}} }{\mathrm{2}}=\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{equal}\:\mathrm{roots},\:\mathrm{prove}\:\mathrm{that}\:{p}^{\mathrm{2}} =\mathrm{4}{q} \\ $$ Commented…
Question Number 113682 by mohammad17 last updated on 14/Sep/20 Commented by mohammad17 last updated on 14/Sep/20 $${thank}\:{you}\:{sir} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 113667 by ZiYangLee last updated on 14/Sep/20 $$\mathrm{In}\:\bigtriangleup\mathrm{ABC},\:\mathrm{BC}=\mathrm{5cm}\:\mathrm{AC}=\mathrm{4cm} \\ $$$$\mathrm{cos}\left(\mathrm{A}−\mathrm{B}\right)=\frac{\mathrm{31}}{\mathrm{32}}\:\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\bigtriangleup\mathrm{ABC}. \\ $$ Answered by som(math1967) last updated on 14/Sep/20 $$\mathrm{tan}^{\mathrm{2}} \frac{\mathrm{A}−\mathrm{B}}{\mathrm{2}}=\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{A}−\mathrm{B}\right)}{\mathrm{1}+\mathrm{cos}\left(\mathrm{A}−\mathrm{B}\right)}…