Question Number 77036 by Master last updated on 02/Jan/20 Commented by mr W last updated on 02/Jan/20 $${if}\:{f}\left(−{x}\right)=−{f}\left({x}\right), \\ $$$$\int_{−{a}} ^{+{a}} {f}\left({x}\right)=\mathrm{0} \\ $$$$\Rightarrow\int_{−\mathrm{1}} ^{+\mathrm{1}}…
Question Number 11501 by @ANTARES_VY last updated on 27/Mar/17 $$\left(\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{7}\boldsymbol{\mathrm{x}}−\mathrm{5}\right)\left(\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{13}\boldsymbol{\mathrm{x}}+\mathrm{3}\right)\left(\mathrm{3}\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{8}\right)=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{all}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{multiples}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{real}}\:\:\boldsymbol{\mathrm{roots}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}. \\ $$ Commented by mrW1 last updated on…
Question Number 11500 by @ANTARES_VY last updated on 27/Mar/17 $$\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}−\mathrm{4}\right)\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\mathrm{4}\right)=\mathrm{9} \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}\:\:\boldsymbol{\mathrm{has}}\:\:\boldsymbol{\mathrm{multiple}}\:\:\boldsymbol{\mathrm{roots}}. \\ $$ Answered by ridwan balatif last updated on 27/Mar/17 $$\left(\left(\mathrm{x}^{\mathrm{2}}…
Question Number 77035 by necxxx last updated on 02/Jan/20 $${Solve}\:{for}\:{x}\:{in}: \\ $$$$\left({i}\right)\:\left(\mathrm{2}\left({x}+\mathrm{3}\right)−\mathrm{3}\left({x}−\mathrm{2}\right)\right)\left(\mathrm{2}{x}−\mathrm{1}\right)\geqslant\mathrm{0} \\ $$$$\left({ii}\right)\left({x}−\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{3}\right)\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right)\leqslant\mathrm{1} \\ $$ Answered by MJS last updated on 03/Jan/20 $$\left({i}\right) \\…
Question Number 142570 by mathsuji last updated on 02/Jun/21 $${Find}\:{all}\:{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:{such}\:{that} \\ $$$${f}\left({x}+{y}\right)=\mathrm{2}{f}\left({x}\right)+\mathrm{3}{f}\left({y}\right)−\mathrm{4}{xyf}\left(\mathrm{2}{x}−\mathrm{3}{y}\right) \\ $$$$\left(\forall{x};{y}\in\mathbb{R}\right) \\ $$ Answered by ajfour last updated on 02/Jun/21 $${f}\left({x}\right)=\mathrm{5}{f}\left(\frac{{x}}{\mathrm{2}}\right)−{x}^{\mathrm{2}} {f}\left(−\frac{{x}}{\mathrm{2}}\right)…
Question Number 77033 by necxxx last updated on 02/Jan/20 $${Suppose}\:{the}\:{population}\:{models}\:{of}\:{London} \\ $$$${and}\:{Hongkong}\:{in}\:{tens}\:{of}\:{thousands}\:{are} \\ $$$${p}\left({t}\right)=\frac{\mathrm{20}{t}}{{t}+\mathrm{1}}\:{and}\:{q}\left({t}\right)=\frac{\mathrm{240}{t}}{{t}+\mathrm{8}}\:{respectively}\:{for} \\ $$$${t}\:{years}\:{after}\:\mathrm{2015},\:{Determine}\:{the}\:{time}\:{period} \\ $$$${in}\:{years}\:{when}\:{the}\:{population}\:{of}\:{London} \\ $$$${exceeds}\:{that}\:{of}\:{HongKong}. \\ $$ Commented by MJS…
Question Number 77028 by TawaTawa last updated on 02/Jan/20 Answered by mind is power last updated on 02/Jan/20 $$\mathrm{39} \\ $$$$\mathrm{x}−\mathrm{y}\:−\mathrm{z}\left(\mathrm{x}−\mathrm{y}\right)=\mathrm{0} \\ $$$$\mathrm{y}−\mathrm{z}−\mathrm{x}\left(\mathrm{y}−\mathrm{z}\right)=\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}}…
Question Number 77026 by TawaTawa last updated on 02/Jan/20 Commented by $@ty@m123 last updated on 03/Jan/20 $${Which}\:{one}? \\ $$$$\mathrm{20}\:{or}\:\mathrm{21} \\ $$ Commented by TawaTawa last…
Question Number 142560 by ajfour last updated on 02/Jun/21 Answered by 1549442205PVT last updated on 02/Jun/21 $$\mathrm{put}\:\mathrm{AC}=\mathrm{x},\mathrm{CP}=\mathrm{y}\Rightarrow\mathrm{AO}.\mathrm{OB}=\mathrm{OP}^{\mathrm{2}} \\ $$$$\Leftrightarrow\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} }\left(\mathrm{1}−\sqrt{\mathrm{c}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} }\right)=\mathrm{c}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \left(\mathrm{1}\right)…
Question Number 77027 by mathocean1 last updated on 02/Jan/20 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\left[−\pi;\mathrm{0}\right] \\ $$$$\mathrm{cos2}{x}+\mathrm{cos}{x}+\mathrm{1}=\mathrm{sin3}{x}+\mathrm{sin2}{x}+\mathrm{sin}{x} \\ $$$${E}\mathrm{xplain}\:\mathrm{details}\:\mathrm{if}\:\mathrm{possible}. \\ $$$$ \\ $$ Answered by mr W last updated on…